---
_id: '72'
abstract:
- lang: eng
text: We consider the totally asymmetric simple exclusion process (TASEP) with non-random
initial condition having density ρ on ℤ− and λ on ℤ+, and a second class particle
initially at the origin. For ρ<λ, there is a shock and the second class particle
moves with speed 1−λ−ρ. For large time t, we show that the position of the second
class particle fluctuates on a t1/3 scale and determine its limiting law. We also
obtain the limiting distribution of the number of steps made by the second class
particle until time t.
article_processing_charge: No
article_type: original
author:
- first_name: Patrick
full_name: Ferrari, Patrick
last_name: Ferrari
- first_name: Promit
full_name: Ghosal, Promit
last_name: Ghosal
- first_name: Peter
full_name: Nejjar, Peter
id: 4BF426E2-F248-11E8-B48F-1D18A9856A87
last_name: Nejjar
citation:
ama: Ferrari P, Ghosal P, Nejjar P. Limit law of a second class particle in TASEP
with non-random initial condition. Annales de l’institut Henri Poincare (B)
Probability and Statistics. 2019;55(3):1203-1225. doi:10.1214/18-AIHP916
apa: Ferrari, P., Ghosal, P., & Nejjar, P. (2019). Limit law of a second class
particle in TASEP with non-random initial condition. Annales de l’institut
Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics.
https://doi.org/10.1214/18-AIHP916
chicago: Ferrari, Patrick, Promit Ghosal, and Peter Nejjar. “Limit Law of a Second
Class Particle in TASEP with Non-Random Initial Condition.” Annales de l’institut
Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics,
2019. https://doi.org/10.1214/18-AIHP916.
ieee: P. Ferrari, P. Ghosal, and P. Nejjar, “Limit law of a second class particle
in TASEP with non-random initial condition,” Annales de l’institut Henri Poincare
(B) Probability and Statistics, vol. 55, no. 3. Institute of Mathematical
Statistics, pp. 1203–1225, 2019.
ista: Ferrari P, Ghosal P, Nejjar P. 2019. Limit law of a second class particle
in TASEP with non-random initial condition. Annales de l’institut Henri Poincare
(B) Probability and Statistics. 55(3), 1203–1225.
mla: Ferrari, Patrick, et al. “Limit Law of a Second Class Particle in TASEP with
Non-Random Initial Condition.” Annales de l’institut Henri Poincare (B) Probability
and Statistics, vol. 55, no. 3, Institute of Mathematical Statistics, 2019,
pp. 1203–25, doi:10.1214/18-AIHP916.
short: P. Ferrari, P. Ghosal, P. Nejjar, Annales de l’institut Henri Poincare (B)
Probability and Statistics 55 (2019) 1203–1225.
date_created: 2018-12-11T11:44:29Z
date_published: 2019-09-25T00:00:00Z
date_updated: 2023-10-17T08:53:45Z
day: '25'
department:
- _id: LaEr
- _id: JaMa
doi: 10.1214/18-AIHP916
ec_funded: 1
external_id:
arxiv:
- '1710.02323'
isi:
- '000487763200001'
intvolume: ' 55'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1710.02323
month: '09'
oa: 1
oa_version: Preprint
page: 1203-1225
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Annales de l'institut Henri Poincare (B) Probability and Statistics
publication_identifier:
issn:
- 0246-0203
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Limit law of a second class particle in TASEP with non-random initial condition
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 55
year: '2019'
...
---
_id: '6240'
abstract:
- lang: eng
text: For a general class of large non-Hermitian random block matrices X we prove
that there are no eigenvalues away from a deterministic set with very high probability.
This set is obtained from the Dyson equation of the Hermitization of X as the
self-consistent approximation of the pseudospectrum. We demonstrate that the analysis
of the matrix Dyson equation from (Probab. Theory Related Fields (2018)) offers
a unified treatment of many structured matrix ensembles.
article_processing_charge: No
author:
- first_name: Johannes
full_name: Alt, Johannes
id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
last_name: Alt
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: Yuriy
full_name: Nemish, Yuriy
id: 4D902E6A-F248-11E8-B48F-1D18A9856A87
last_name: Nemish
orcid: 0000-0002-7327-856X
citation:
ama: Alt J, Erdös L, Krüger TH, Nemish Y. Location of the spectrum of Kronecker
random matrices. Annales de l’institut Henri Poincare. 2019;55(2):661-696.
doi:10.1214/18-AIHP894
apa: Alt, J., Erdös, L., Krüger, T. H., & Nemish, Y. (2019). Location of the
spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare.
Institut Henri Poincaré. https://doi.org/10.1214/18-AIHP894
chicago: Alt, Johannes, László Erdös, Torben H Krüger, and Yuriy Nemish. “Location
of the Spectrum of Kronecker Random Matrices.” Annales de l’institut Henri
Poincare. Institut Henri Poincaré, 2019. https://doi.org/10.1214/18-AIHP894.
ieee: J. Alt, L. Erdös, T. H. Krüger, and Y. Nemish, “Location of the spectrum of
Kronecker random matrices,” Annales de l’institut Henri Poincare, vol.
55, no. 2. Institut Henri Poincaré, pp. 661–696, 2019.
ista: Alt J, Erdös L, Krüger TH, Nemish Y. 2019. Location of the spectrum of Kronecker
random matrices. Annales de l’institut Henri Poincare. 55(2), 661–696.
mla: Alt, Johannes, et al. “Location of the Spectrum of Kronecker Random Matrices.”
Annales de l’institut Henri Poincare, vol. 55, no. 2, Institut Henri Poincaré,
2019, pp. 661–96, doi:10.1214/18-AIHP894.
short: J. Alt, L. Erdös, T.H. Krüger, Y. Nemish, Annales de l’institut Henri Poincare
55 (2019) 661–696.
date_created: 2019-04-08T14:05:04Z
date_published: 2019-05-01T00:00:00Z
date_updated: 2023-10-17T12:20:20Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/18-AIHP894
ec_funded: 1
external_id:
arxiv:
- '1706.08343'
isi:
- '000467793600003'
intvolume: ' 55'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1706.08343
month: '05'
oa: 1
oa_version: Preprint
page: 661-696
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Annales de l'institut Henri Poincare
publication_identifier:
issn:
- 0246-0203
publication_status: published
publisher: Institut Henri Poincaré
quality_controlled: '1'
related_material:
record:
- id: '149'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Location of the spectrum of Kronecker random matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 55
year: '2019'
...
---
_id: '6179'
abstract:
- lang: eng
text: "In the first part of this thesis we consider large random matrices with arbitrary
expectation and a general slowly decaying correlation among its entries. We prove
universality of the local eigenvalue statistics and optimal local laws for the
resolvent in the bulk and edge regime. The main novel tool is a systematic diagrammatic
control of a multivariate cumulant expansion.\r\nIn the second part we consider
Wigner-type matrices and show that at any cusp singularity of the limiting eigenvalue
distribution the local eigenvalue statistics are uni- versal and form a Pearcey
process. Since the density of states typically exhibits only square root or cubic
root cusp singularities, our work complements previous results on the bulk and
edge universality and it thus completes the resolution of the Wigner- Dyson-Mehta
universality conjecture for the last remaining universality type. Our analysis
holds not only for exact cusps, but approximate cusps as well, where an ex- tended
Pearcey process emerges. As a main technical ingredient we prove an optimal local
law at the cusp, and extend the fast relaxation to equilibrium of the Dyson Brow-
nian motion to the cusp regime.\r\nIn the third and final part we explore the
entrywise linear statistics of Wigner ma- trices and identify the fluctuations
for a large class of test functions with little regularity. This enables us to
study the rectangular Young diagram obtained from the interlacing eigenvalues
of the random matrix and its minor, and we find that, despite having the same
limit, the fluctuations differ from those of the algebraic Young tableaux equipped
with the Plancharel measure."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: 'Schröder DJ. From Dyson to Pearcey: Universal statistics in random matrix
theory. 2019. doi:10.15479/AT:ISTA:th6179'
apa: 'Schröder, D. J. (2019). From Dyson to Pearcey: Universal statistics in
random matrix theory. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th6179'
chicago: 'Schröder, Dominik J. “From Dyson to Pearcey: Universal Statistics in Random
Matrix Theory.” Institute of Science and Technology Austria, 2019. https://doi.org/10.15479/AT:ISTA:th6179.'
ieee: 'D. J. Schröder, “From Dyson to Pearcey: Universal statistics in random matrix
theory,” Institute of Science and Technology Austria, 2019.'
ista: 'Schröder DJ. 2019. From Dyson to Pearcey: Universal statistics in random
matrix theory. Institute of Science and Technology Austria.'
mla: 'Schröder, Dominik J. From Dyson to Pearcey: Universal Statistics in Random
Matrix Theory. Institute of Science and Technology Austria, 2019, doi:10.15479/AT:ISTA:th6179.'
short: 'D.J. Schröder, From Dyson to Pearcey: Universal Statistics in Random Matrix
Theory, Institute of Science and Technology Austria, 2019.'
date_created: 2019-03-28T08:58:59Z
date_published: 2019-03-18T00:00:00Z
date_updated: 2024-02-22T14:34:33Z
day: '18'
ddc:
- '515'
- '519'
degree_awarded: PhD
department:
- _id: LaEr
doi: 10.15479/AT:ISTA:th6179
ec_funded: 1
file:
- access_level: closed
checksum: 6926f66f28079a81c4937e3764be00fc
content_type: application/x-gzip
creator: dernst
date_created: 2019-03-28T08:53:52Z
date_updated: 2020-07-14T12:47:21Z
file_id: '6180'
file_name: 2019_Schroeder_Thesis.tar.gz
file_size: 7104482
relation: source_file
- access_level: open_access
checksum: 7d0ebb8d1207e89768cdd497a5bf80fb
content_type: application/pdf
creator: dernst
date_created: 2019-03-28T08:53:52Z
date_updated: 2020-07-14T12:47:21Z
file_id: '6181'
file_name: 2019_Schroeder_Thesis.pdf
file_size: 4228794
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file_date_updated: 2020-07-14T12:47:21Z
has_accepted_license: '1'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: '375'
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '1144'
relation: part_of_dissertation
status: public
- id: '6186'
relation: part_of_dissertation
status: public
- id: '6185'
relation: part_of_dissertation
status: public
- id: '6182'
relation: part_of_dissertation
status: public
- id: '1012'
relation: part_of_dissertation
status: public
- id: '6184'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
title: 'From Dyson to Pearcey: Universal statistics in random matrix theory'
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2019'
...
---
_id: '690'
abstract:
- lang: eng
text: We consider spectral properties and the edge universality of sparse random
matrices, the class of random matrices that includes the adjacency matrices of
the Erdős–Rényi graph model G(N, p). We prove a local law for the eigenvalue density
up to the spectral edges. Under a suitable condition on the sparsity, we also
prove that the rescaled extremal eigenvalues exhibit GOE Tracy–Widom fluctuations
if a deterministic shift of the spectral edge due to the sparsity is included.
For the adjacency matrix of the Erdős–Rényi graph this establishes the Tracy–Widom
fluctuations of the second largest eigenvalue when p is much larger than N−2/3
with a deterministic shift of order (Np)−1.
article_number: 543-616
author:
- first_name: Jii
full_name: Lee, Jii
last_name: Lee
- first_name: Kevin
full_name: Schnelli, Kevin
id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
last_name: Schnelli
orcid: 0000-0003-0954-3231
citation:
ama: Lee J, Schnelli K. Local law and Tracy–Widom limit for sparse random matrices.
Probability Theory and Related Fields. 2018;171(1-2). doi:10.1007/s00440-017-0787-8
apa: Lee, J., & Schnelli, K. (2018). Local law and Tracy–Widom limit for sparse
random matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-017-0787-8
chicago: Lee, Jii, and Kevin Schnelli. “Local Law and Tracy–Widom Limit for Sparse
Random Matrices.” Probability Theory and Related Fields. Springer, 2018.
https://doi.org/10.1007/s00440-017-0787-8.
ieee: J. Lee and K. Schnelli, “Local law and Tracy–Widom limit for sparse random
matrices,” Probability Theory and Related Fields, vol. 171, no. 1–2. Springer,
2018.
ista: Lee J, Schnelli K. 2018. Local law and Tracy–Widom limit for sparse random
matrices. Probability Theory and Related Fields. 171(1–2), 543–616.
mla: Lee, Jii, and Kevin Schnelli. “Local Law and Tracy–Widom Limit for Sparse Random
Matrices.” Probability Theory and Related Fields, vol. 171, no. 1–2, 543–616,
Springer, 2018, doi:10.1007/s00440-017-0787-8.
short: J. Lee, K. Schnelli, Probability Theory and Related Fields 171 (2018).
date_created: 2018-12-11T11:47:56Z
date_published: 2018-06-14T00:00:00Z
date_updated: 2021-01-12T08:09:33Z
day: '14'
department:
- _id: LaEr
doi: 10.1007/s00440-017-0787-8
ec_funded: 1
external_id:
arxiv:
- '1605.08767'
intvolume: ' 171'
issue: 1-2
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1605.08767
month: '06'
oa: 1
oa_version: Preprint
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Probability Theory and Related Fields
publication_status: published
publisher: Springer
publist_id: '7017'
quality_controlled: '1'
scopus_import: 1
status: public
title: Local law and Tracy–Widom limit for sparse random matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 171
year: '2018'
...
---
_id: '566'
abstract:
- lang: eng
text: "We consider large random matrices X with centered, independent entries which
have comparable but not necessarily identical variances. Girko's circular law
asserts that the spectrum is supported in a disk and in case of identical variances,
the limiting density is uniform. In this special case, the local circular law
by Bourgade et. al. [11,12] shows that the empirical density converges even locally
on scales slightly above the typical eigenvalue spacing. In the general case,
the limiting density is typically inhomogeneous and it is obtained via solving
a system of deterministic equations. Our main result is the local inhomogeneous
circular law in the bulk spectrum on the optimal scale for a general variance
profile of the entries of X. \r\n\r\n"
article_processing_charge: No
article_type: original
author:
- first_name: Johannes
full_name: Alt, Johannes
id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
last_name: Alt
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
citation:
ama: Alt J, Erdös L, Krüger TH. Local inhomogeneous circular law. Annals Applied
Probability . 2018;28(1):148-203. doi:10.1214/17-AAP1302
apa: Alt, J., Erdös, L., & Krüger, T. H. (2018). Local inhomogeneous circular
law. Annals Applied Probability . Institute of Mathematical Statistics.
https://doi.org/10.1214/17-AAP1302
chicago: Alt, Johannes, László Erdös, and Torben H Krüger. “Local Inhomogeneous
Circular Law.” Annals Applied Probability . Institute of Mathematical Statistics,
2018. https://doi.org/10.1214/17-AAP1302.
ieee: J. Alt, L. Erdös, and T. H. Krüger, “Local inhomogeneous circular law,” Annals
Applied Probability , vol. 28, no. 1. Institute of Mathematical Statistics,
pp. 148–203, 2018.
ista: Alt J, Erdös L, Krüger TH. 2018. Local inhomogeneous circular law. Annals
Applied Probability . 28(1), 148–203.
mla: Alt, Johannes, et al. “Local Inhomogeneous Circular Law.” Annals Applied
Probability , vol. 28, no. 1, Institute of Mathematical Statistics, 2018,
pp. 148–203, doi:10.1214/17-AAP1302.
short: J. Alt, L. Erdös, T.H. Krüger, Annals Applied Probability 28 (2018) 148–203.
date_created: 2018-12-11T11:47:13Z
date_published: 2018-03-03T00:00:00Z
date_updated: 2023-09-13T08:47:52Z
day: '03'
department:
- _id: LaEr
doi: 10.1214/17-AAP1302
ec_funded: 1
external_id:
arxiv:
- '1612.07776 '
isi:
- '000431721800005'
intvolume: ' 28'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: 'https://arxiv.org/abs/1612.07776 '
month: '03'
oa: 1
oa_version: Preprint
page: 148-203
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: 'Annals Applied Probability '
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
related_material:
record:
- id: '149'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Local inhomogeneous circular law
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 28
year: '2018'
...
---
_id: '181'
abstract:
- lang: eng
text: We consider large random matrices X with centered, independent entries but
possibly di erent variances. We compute the normalized trace of f(X)g(X∗) for
f, g functions analytic on the spectrum of X. We use these results to compute
the long time asymptotics for systems of coupled di erential equations with random
coe cients. We show that when the coupling is critical, the norm squared of the
solution decays like t−1/2.
acknowledgement: The work of the second author was also partially supported by the
Hausdorff Center of Mathematics.
article_processing_charge: No
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: David T
full_name: Renfrew, David T
id: 4845BF6A-F248-11E8-B48F-1D18A9856A87
last_name: Renfrew
orcid: 0000-0003-3493-121X
citation:
ama: Erdös L, Krüger TH, Renfrew DT. Power law decay for systems of randomly coupled
differential equations. SIAM Journal on Mathematical Analysis. 2018;50(3):3271-3290.
doi:10.1137/17M1143125
apa: Erdös, L., Krüger, T. H., & Renfrew, D. T. (2018). Power law decay for
systems of randomly coupled differential equations. SIAM Journal on Mathematical
Analysis. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/17M1143125
chicago: Erdös, László, Torben H Krüger, and David T Renfrew. “Power Law Decay for
Systems of Randomly Coupled Differential Equations.” SIAM Journal on Mathematical
Analysis. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/17M1143125.
ieee: L. Erdös, T. H. Krüger, and D. T. Renfrew, “Power law decay for systems of
randomly coupled differential equations,” SIAM Journal on Mathematical Analysis,
vol. 50, no. 3. Society for Industrial and Applied Mathematics , pp. 3271–3290,
2018.
ista: Erdös L, Krüger TH, Renfrew DT. 2018. Power law decay for systems of randomly
coupled differential equations. SIAM Journal on Mathematical Analysis. 50(3),
3271–3290.
mla: Erdös, László, et al. “Power Law Decay for Systems of Randomly Coupled Differential
Equations.” SIAM Journal on Mathematical Analysis, vol. 50, no. 3, Society
for Industrial and Applied Mathematics , 2018, pp. 3271–90, doi:10.1137/17M1143125.
short: L. Erdös, T.H. Krüger, D.T. Renfrew, SIAM Journal on Mathematical Analysis
50 (2018) 3271–3290.
date_created: 2018-12-11T11:45:03Z
date_published: 2018-01-01T00:00:00Z
date_updated: 2023-09-15T12:05:52Z
day: '01'
department:
- _id: LaEr
doi: 10.1137/17M1143125
ec_funded: 1
external_id:
arxiv:
- '1708.01546'
isi:
- '000437018500032'
intvolume: ' 50'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1708.01546
month: '01'
oa: 1
oa_version: Published Version
page: 3271 - 3290
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 258F40A4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M02080
name: Structured Non-Hermitian Random Matrices
publication: SIAM Journal on Mathematical Analysis
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
publist_id: '7740'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Power law decay for systems of randomly coupled differential equations
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 50
year: '2018'
...
---
_id: '5971'
abstract:
- lang: eng
text: "We consider a Wigner-type ensemble, i.e. large hermitian N×N random matrices
H=H∗ with centered independent entries and with a general matrix of variances
Sxy=\U0001D53C∣∣Hxy∣∣2. The norm of H is asymptotically given by the maximum of
the support of the self-consistent density of states. We establish a bound on
this maximum in terms of norms of powers of S that substantially improves the
earlier bound 2∥S∥1/2∞ given in [O. Ajanki, L. Erdős and T. Krüger, Universality
for general Wigner-type matrices, Prob. Theor. Rel. Fields169 (2017) 667–727].
The key element of the proof is an effective Markov chain approximation for the
contributions of the weighted Dyck paths appearing in the iterative solution of
the corresponding Dyson equation."
article_number: '1950009'
article_processing_charge: No
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Peter
full_name: Mühlbacher, Peter
last_name: Mühlbacher
citation:
ama: 'Erdös L, Mühlbacher P. Bounds on the norm of Wigner-type random matrices.
Random matrices: Theory and applications. 2018. doi:10.1142/s2010326319500096'
apa: 'Erdös, L., & Mühlbacher, P. (2018). Bounds on the norm of Wigner-type
random matrices. Random Matrices: Theory and Applications. World Scientific
Publishing. https://doi.org/10.1142/s2010326319500096'
chicago: 'Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type
Random Matrices.” Random Matrices: Theory and Applications. World Scientific
Publishing, 2018. https://doi.org/10.1142/s2010326319500096.'
ieee: 'L. Erdös and P. Mühlbacher, “Bounds on the norm of Wigner-type random matrices,”
Random matrices: Theory and applications. World Scientific Publishing,
2018.'
ista: 'Erdös L, Mühlbacher P. 2018. Bounds on the norm of Wigner-type random matrices.
Random matrices: Theory and applications., 1950009.'
mla: 'Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random
Matrices.” Random Matrices: Theory and Applications, 1950009, World Scientific
Publishing, 2018, doi:10.1142/s2010326319500096.'
short: 'L. Erdös, P. Mühlbacher, Random Matrices: Theory and Applications (2018).'
date_created: 2019-02-13T10:40:54Z
date_published: 2018-09-26T00:00:00Z
date_updated: 2023-09-19T14:24:05Z
day: '26'
department:
- _id: LaEr
doi: 10.1142/s2010326319500096
ec_funded: 1
external_id:
arxiv:
- '1802.05175'
isi:
- '000477677200002'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1802.05175
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: 'Random matrices: Theory and applications'
publication_identifier:
eissn:
- 2010-3271
issn:
- 2010-3263
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bounds on the norm of Wigner-type random matrices
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2018'
...
---
_id: '1012'
abstract:
- lang: eng
text: We prove a new central limit theorem (CLT) for the difference of linear eigenvalue
statistics of a Wigner random matrix H and its minor H and find that the fluctuation
is much smaller than the fluctuations of the individual linear statistics, as
a consequence of the strong correlation between the eigenvalues of H and H. In
particular, our theorem identifies the fluctuation of Kerov's rectangular Young
diagrams, defined by the interlacing eigenvalues ofH and H, around their asymptotic
shape, the Vershik'Kerov'Logan'Shepp curve. Young diagrams equipped with the Plancherel
measure follow the same limiting shape. For this, algebraically motivated, ensemble
a CLT has been obtained in Ivanov and Olshanski [20] which is structurally similar
to our result but the variance is different, indicating that the analogy between
the two models has its limitations. Moreover, our theorem shows that Borodin's
result [7] on the convergence of the spectral distribution of Wigner matrices
to a Gaussian free field also holds in derivative sense.
article_processing_charge: No
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: Erdös L, Schröder DJ. Fluctuations of rectangular young diagrams of interlacing
wigner eigenvalues. International Mathematics Research Notices. 2018;2018(10):3255-3298.
doi:10.1093/imrn/rnw330
apa: Erdös, L., & Schröder, D. J. (2018). Fluctuations of rectangular young
diagrams of interlacing wigner eigenvalues. International Mathematics Research
Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnw330
chicago: Erdös, László, and Dominik J Schröder. “Fluctuations of Rectangular Young
Diagrams of Interlacing Wigner Eigenvalues.” International Mathematics Research
Notices. Oxford University Press, 2018. https://doi.org/10.1093/imrn/rnw330.
ieee: L. Erdös and D. J. Schröder, “Fluctuations of rectangular young diagrams of
interlacing wigner eigenvalues,” International Mathematics Research Notices,
vol. 2018, no. 10. Oxford University Press, pp. 3255–3298, 2018.
ista: Erdös L, Schröder DJ. 2018. Fluctuations of rectangular young diagrams of
interlacing wigner eigenvalues. International Mathematics Research Notices. 2018(10),
3255–3298.
mla: Erdös, László, and Dominik J. Schröder. “Fluctuations of Rectangular Young
Diagrams of Interlacing Wigner Eigenvalues.” International Mathematics Research
Notices, vol. 2018, no. 10, Oxford University Press, 2018, pp. 3255–98, doi:10.1093/imrn/rnw330.
short: L. Erdös, D.J. Schröder, International Mathematics Research Notices 2018
(2018) 3255–3298.
date_created: 2018-12-11T11:49:41Z
date_published: 2018-05-18T00:00:00Z
date_updated: 2023-09-22T09:44:21Z
day: '18'
department:
- _id: LaEr
doi: 10.1093/imrn/rnw330
ec_funded: 1
external_id:
arxiv:
- '1608.05163'
isi:
- '000441668300009'
intvolume: ' 2018'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1608.05163
month: '05'
oa: 1
oa_version: Preprint
page: 3255-3298
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: International Mathematics Research Notices
publication_identifier:
issn:
- '10737928'
publication_status: published
publisher: Oxford University Press
publist_id: '6383'
quality_controlled: '1'
related_material:
record:
- id: '6179'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 2018
year: '2018'
...
---
_id: '70'
abstract:
- lang: eng
text: We consider the totally asymmetric simple exclusion process in a critical
scaling parametrized by a≥0, which creates a shock in the particle density of
order aT−1/3, T the observation time. When starting from step initial data, we
provide bounds on the limiting law which in particular imply that in the double
limit lima→∞limT→∞ one recovers the product limit law and the degeneration of
the correlation length observed at shocks of order 1. This result is shown to
apply to a general last-passage percolation model. We also obtain bounds on the
two-point functions of several airy processes.
article_processing_charge: No
article_type: original
author:
- first_name: Peter
full_name: Nejjar, Peter
id: 4BF426E2-F248-11E8-B48F-1D18A9856A87
last_name: Nejjar
citation:
ama: Nejjar P. Transition to shocks in TASEP and decoupling of last passage times.
Latin American Journal of Probability and Mathematical Statistics. 2018;15(2):1311-1334.
doi:10.30757/ALEA.v15-49
apa: Nejjar, P. (2018). Transition to shocks in TASEP and decoupling of last passage
times. Latin American Journal of Probability and Mathematical Statistics.
Instituto Nacional de Matematica Pura e Aplicada. https://doi.org/10.30757/ALEA.v15-49
chicago: Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage
Times.” Latin American Journal of Probability and Mathematical Statistics.
Instituto Nacional de Matematica Pura e Aplicada, 2018. https://doi.org/10.30757/ALEA.v15-49.
ieee: P. Nejjar, “Transition to shocks in TASEP and decoupling of last passage times,”
Latin American Journal of Probability and Mathematical Statistics, vol.
15, no. 2. Instituto Nacional de Matematica Pura e Aplicada, pp. 1311–1334, 2018.
ista: Nejjar P. 2018. Transition to shocks in TASEP and decoupling of last passage
times. Latin American Journal of Probability and Mathematical Statistics. 15(2),
1311–1334.
mla: Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage
Times.” Latin American Journal of Probability and Mathematical Statistics,
vol. 15, no. 2, Instituto Nacional de Matematica Pura e Aplicada, 2018, pp. 1311–34,
doi:10.30757/ALEA.v15-49.
short: P. Nejjar, Latin American Journal of Probability and Mathematical Statistics
15 (2018) 1311–1334.
date_created: 2018-12-11T11:44:28Z
date_published: 2018-10-01T00:00:00Z
date_updated: 2023-10-10T13:11:29Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
- _id: JaMa
doi: 10.30757/ALEA.v15-49
ec_funded: 1
external_id:
arxiv:
- '1705.08836'
isi:
- '000460475800022'
file:
- access_level: open_access
checksum: 2ded46aa284a836a8cbb34133a64f1cb
content_type: application/pdf
creator: kschuh
date_created: 2019-02-14T09:44:10Z
date_updated: 2020-07-14T12:47:46Z
file_id: '5981'
file_name: 2018_ALEA_Nejjar.pdf
file_size: 394851
relation: main_file
file_date_updated: 2020-07-14T12:47:46Z
has_accepted_license: '1'
intvolume: ' 15'
isi: 1
issue: '2'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 1311-1334
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Latin American Journal of Probability and Mathematical Statistics
publication_identifier:
issn:
- 1980-0436
publication_status: published
publisher: Instituto Nacional de Matematica Pura e Aplicada
quality_controlled: '1'
scopus_import: '1'
status: public
title: Transition to shocks in TASEP and decoupling of last passage times
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 15
year: '2018'
...
---
_id: '284'
abstract:
- lang: eng
text: "Borel probability measures living on metric spaces are fundamental\r\nmathematical
objects. There are several meaningful distance functions that make the collection
of the probability measures living on a certain space a metric space. We are interested
in the description of the structure of the isometries of such metric spaces. We
overview some of the recent results of the topic and we also provide some new
ones concerning the Wasserstein distance. More specifically, we consider the space
of all Borel probability measures on the unit sphere of a Euclidean space endowed
with the Wasserstein metric W_p for arbitrary p >= 1, and we show that the
action of a Wasserstein isometry on the set of Dirac measures is induced by an
isometry of the underlying unit sphere."
acknowledgement: The author was supported by the ISTFELLOW program of the Institute
of Science and Technol- ogy Austria (project code IC1027FELL01) and partially supported
by the Hungarian National Research, Development and Innovation Office, NKFIH (grant
no. K124152).
article_processing_charge: No
article_type: original
author:
- first_name: Daniel
full_name: Virosztek, Daniel
id: 48DB45DA-F248-11E8-B48F-1D18A9856A87
last_name: Virosztek
orcid: 0000-0003-1109-5511
citation:
ama: Virosztek D. Maps on probability measures preserving certain distances - a
survey and some new results. Acta Scientiarum Mathematicarum. 2018;84(1-2):65-80.
doi:10.14232/actasm-018-753-y
apa: Virosztek, D. (2018). Maps on probability measures preserving certain distances
- a survey and some new results. Acta Scientiarum Mathematicarum. Springer
Nature. https://doi.org/10.14232/actasm-018-753-y
chicago: Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances
- a Survey and Some New Results.” Acta Scientiarum Mathematicarum. Springer
Nature, 2018. https://doi.org/10.14232/actasm-018-753-y.
ieee: D. Virosztek, “Maps on probability measures preserving certain distances -
a survey and some new results,” Acta Scientiarum Mathematicarum, vol. 84,
no. 1–2. Springer Nature, pp. 65–80, 2018.
ista: Virosztek D. 2018. Maps on probability measures preserving certain distances
- a survey and some new results. Acta Scientiarum Mathematicarum. 84(1–2), 65–80.
mla: Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances
- a Survey and Some New Results.” Acta Scientiarum Mathematicarum, vol.
84, no. 1–2, Springer Nature, 2018, pp. 65–80, doi:10.14232/actasm-018-753-y.
short: D. Virosztek, Acta Scientiarum Mathematicarum 84 (2018) 65–80.
date_created: 2018-12-11T11:45:36Z
date_published: 2018-06-04T00:00:00Z
date_updated: 2023-10-16T10:29:22Z
day: '04'
department:
- _id: LaEr
doi: 10.14232/actasm-018-753-y
ec_funded: 1
external_id:
arxiv:
- '1802.03305'
intvolume: ' 84'
issue: 1-2
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1802.03305
month: '06'
oa: 1
oa_version: Preprint
page: 65 - 80
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Acta Scientiarum Mathematicarum
publication_identifier:
eissn:
- 2064-8316
issn:
- 0001-6969
publication_status: published
publisher: Springer Nature
publist_id: '7615'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Maps on probability measures preserving certain distances - a survey and some
new results
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 84
year: '2018'
...
---
_id: '6183'
abstract:
- lang: eng
text: "We study the unique solution $m$ of the Dyson equation \\[ -m(z)^{-1} = z
- a\r\n+ S[m(z)] \\] on a von Neumann algebra $\\mathcal{A}$ with the constraint\r\n$\\mathrm{Im}\\,m\\geq
0$. Here, $z$ lies in the complex upper half-plane, $a$ is\r\na self-adjoint element
of $\\mathcal{A}$ and $S$ is a positivity-preserving\r\nlinear operator on $\\mathcal{A}$.
We show that $m$ is the Stieltjes transform\r\nof a compactly supported $\\mathcal{A}$-valued
measure on $\\mathbb{R}$. Under\r\nsuitable assumptions, we establish that this
measure has a uniformly\r\n$1/3$-H\\\"{o}lder continuous density with respect
to the Lebesgue measure, which\r\nis supported on finitely many intervals, called
bands. In fact, the density is\r\nanalytic inside the bands with a square-root
growth at the edges and internal\r\ncubic root cusps whenever the gap between
two bands vanishes. The shape of\r\nthese singularities is universal and no other
singularity may occur. We give a\r\nprecise asymptotic description of $m$ near
the singular points. These\r\nasymptotics generalize the analysis at the regular
edges given in the companion\r\npaper on the Tracy-Widom universality for the
edge eigenvalue statistics for\r\ncorrelated random matrices [arXiv:1804.07744]
and they play a key role in the\r\nproof of the Pearcey universality at the cusp
for Wigner-type matrices\r\n[arXiv:1809.03971,arXiv:1811.04055]. We also extend
the finite dimensional band\r\nmass formula from [arXiv:1804.07744] to the von
Neumann algebra setting by\r\nshowing that the spectral mass of the bands is topologically
rigid under\r\ndeformations and we conclude that these masses are quantized in
some important\r\ncases."
article_number: '1804.07752'
article_processing_charge: No
author:
- first_name: Johannes
full_name: Alt, Johannes
id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
last_name: Alt
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
citation:
ama: 'Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral
bands, edges and cusps. arXiv.'
apa: 'Alt, J., Erdös, L., & Krüger, T. H. (n.d.). The Dyson equation with linear
self-energy: Spectral bands, edges and cusps. arXiv.'
chicago: 'Alt, Johannes, László Erdös, and Torben H Krüger. “The Dyson Equation
with Linear Self-Energy: Spectral Bands, Edges and Cusps.” ArXiv, n.d.'
ieee: 'J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy:
Spectral bands, edges and cusps,” arXiv. .'
ista: 'Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral
bands, edges and cusps. arXiv, 1804.07752.'
mla: 'Alt, Johannes, et al. “The Dyson Equation with Linear Self-Energy: Spectral
Bands, Edges and Cusps.” ArXiv, 1804.07752.'
short: J. Alt, L. Erdös, T.H. Krüger, ArXiv (n.d.).
date_created: 2019-03-28T09:20:06Z
date_published: 2018-04-20T00:00:00Z
date_updated: 2023-12-18T10:46:08Z
day: '20'
department:
- _id: LaEr
external_id:
arxiv:
- '1804.07752'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1804.07752
month: '04'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: submitted
related_material:
record:
- id: '149'
relation: dissertation_contains
status: public
- id: '14694'
relation: later_version
status: public
status: public
title: 'The Dyson equation with linear self-energy: Spectral bands, edges and cusps'
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2018'
...
---
_id: '556'
abstract:
- lang: eng
text: 'We investigate the free boundary Schur process, a variant of the Schur process
introduced by Okounkov and Reshetikhin, where we allow the first and the last
partitions to be arbitrary (instead of empty in the original setting). The pfaffian
Schur process, previously studied by several authors, is recovered when just one
of the boundary partitions is left free. We compute the correlation functions
of the process in all generality via the free fermion formalism, which we extend
with the thorough treatment of “free boundary states.” For the case of one free
boundary, our approach yields a new proof that the process is pfaffian. For the
case of two free boundaries, we find that the process is not pfaffian, but a closely
related process is. We also study three different applications of the Schur process
with one free boundary: fluctuations of symmetrized last passage percolation models,
limit shapes and processes for symmetric plane partitions and for plane overpartitions.'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Dan
full_name: Betea, Dan
last_name: Betea
- first_name: Jeremie
full_name: Bouttier, Jeremie
last_name: Bouttier
- first_name: Peter
full_name: Nejjar, Peter
id: 4BF426E2-F248-11E8-B48F-1D18A9856A87
last_name: Nejjar
- first_name: Mirjana
full_name: Vuletic, Mirjana
last_name: Vuletic
citation:
ama: Betea D, Bouttier J, Nejjar P, Vuletic M. The free boundary Schur process and
applications I. Annales Henri Poincare. 2018;19(12):3663-3742. doi:10.1007/s00023-018-0723-1
apa: Betea, D., Bouttier, J., Nejjar, P., & Vuletic, M. (2018). The free boundary
Schur process and applications I. Annales Henri Poincare. Springer Nature.
https://doi.org/10.1007/s00023-018-0723-1
chicago: Betea, Dan, Jeremie Bouttier, Peter Nejjar, and Mirjana Vuletic. “The Free
Boundary Schur Process and Applications I.” Annales Henri Poincare. Springer
Nature, 2018. https://doi.org/10.1007/s00023-018-0723-1.
ieee: D. Betea, J. Bouttier, P. Nejjar, and M. Vuletic, “The free boundary Schur
process and applications I,” Annales Henri Poincare, vol. 19, no. 12. Springer
Nature, pp. 3663–3742, 2018.
ista: Betea D, Bouttier J, Nejjar P, Vuletic M. 2018. The free boundary Schur process
and applications I. Annales Henri Poincare. 19(12), 3663–3742.
mla: Betea, Dan, et al. “The Free Boundary Schur Process and Applications I.” Annales
Henri Poincare, vol. 19, no. 12, Springer Nature, 2018, pp. 3663–742, doi:10.1007/s00023-018-0723-1.
short: D. Betea, J. Bouttier, P. Nejjar, M. Vuletic, Annales Henri Poincare 19 (2018)
3663–3742.
date_created: 2018-12-11T11:47:09Z
date_published: 2018-11-13T00:00:00Z
date_updated: 2024-02-20T10:48:17Z
day: '13'
ddc:
- '500'
department:
- _id: LaEr
- _id: JaMa
doi: 10.1007/s00023-018-0723-1
ec_funded: 1
external_id:
arxiv:
- '1704.05809'
file:
- access_level: open_access
checksum: 0c38abe73569b7166b7487ad5d23cc68
content_type: application/pdf
creator: dernst
date_created: 2019-01-21T15:18:55Z
date_updated: 2020-07-14T12:47:03Z
file_id: '5866'
file_name: 2018_Annales_Betea.pdf
file_size: 3084674
relation: main_file
file_date_updated: 2020-07-14T12:47:03Z
has_accepted_license: '1'
intvolume: ' 19'
issue: '12'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 3663-3742
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Annales Henri Poincare
publication_identifier:
issn:
- 1424-0637
publication_status: published
publisher: Springer Nature
publist_id: '7258'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The free boundary Schur process and applications I
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 19
year: '2018'
...
---
_id: '149'
abstract:
- lang: eng
text: The eigenvalue density of many large random matrices is well approximated
by a deterministic measure, the self-consistent density of states. In the present
work, we show this behaviour for several classes of random matrices. In fact,
we establish that, in each of these classes, the self-consistent density of states
approximates the eigenvalue density of the random matrix on all scales slightly
above the typical eigenvalue spacing. For large classes of random matrices, the
self-consistent density of states exhibits several universal features. We prove
that, under suitable assumptions, random Gram matrices and Hermitian random matrices
with decaying correlations have a 1/3-Hölder continuous self-consistent density
of states ρ on R, which is analytic, where it is positive, and has either a square
root edge or a cubic root cusp, where it vanishes. We, thus, extend the validity
of the corresponding result for Wigner-type matrices from [4, 5, 7]. We show that
ρ is determined as the inverse Stieltjes transform of the normalized trace of
the unique solution m(z) to the Dyson equation −m(z) −1 = z − a + S[m(z)] on C
N×N with the constraint Im m(z) ≥ 0. Here, z lies in the complex upper half-plane,
a is a self-adjoint element of C N×N and S is a positivity-preserving operator
on C N×N encoding the first two moments of the random matrix. In order to analyze
a possible limit of ρ for N → ∞ and address some applications in free probability
theory, we also consider the Dyson equation on infinite dimensional von Neumann
algebras. We present two applications to random matrices. We first establish that,
under certain assumptions, large random matrices with independent entries have
a rotationally symmetric self-consistent density of states which is supported
on a centered disk in C. Moreover, it is infinitely often differentiable apart
from a jump on the boundary of this disk. Second, we show edge universality at
all regular (not necessarily extreme) spectral edges for Hermitian random matrices
with decaying correlations.
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Johannes
full_name: Alt, Johannes
id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
last_name: Alt
citation:
ama: Alt J. Dyson equation and eigenvalue statistics of random matrices. 2018. doi:10.15479/AT:ISTA:TH_1040
apa: Alt, J. (2018). Dyson equation and eigenvalue statistics of random matrices.
Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:TH_1040
chicago: Alt, Johannes. “Dyson Equation and Eigenvalue Statistics of Random Matrices.”
Institute of Science and Technology Austria, 2018. https://doi.org/10.15479/AT:ISTA:TH_1040.
ieee: J. Alt, “Dyson equation and eigenvalue statistics of random matrices,” Institute
of Science and Technology Austria, 2018.
ista: Alt J. 2018. Dyson equation and eigenvalue statistics of random matrices.
Institute of Science and Technology Austria.
mla: Alt, Johannes. Dyson Equation and Eigenvalue Statistics of Random Matrices.
Institute of Science and Technology Austria, 2018, doi:10.15479/AT:ISTA:TH_1040.
short: J. Alt, Dyson Equation and Eigenvalue Statistics of Random Matrices, Institute
of Science and Technology Austria, 2018.
date_created: 2018-12-11T11:44:53Z
date_published: 2018-07-12T00:00:00Z
date_updated: 2024-02-22T14:34:33Z
day: '12'
ddc:
- '515'
- '519'
degree_awarded: PhD
department:
- _id: LaEr
doi: 10.15479/AT:ISTA:TH_1040
ec_funded: 1
file:
- access_level: open_access
checksum: d4dad55a7513f345706aaaba90cb1bb8
content_type: application/pdf
creator: dernst
date_created: 2019-04-08T13:55:20Z
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file_name: 2018_thesis_Alt.pdf
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creator: dernst
date_created: 2019-04-08T13:55:20Z
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file_name: 2018_thesis_Alt_source.zip
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language:
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month: '07'
oa: 1
oa_version: Published Version
page: '456'
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
publist_id: '7772'
pubrep_id: '1040'
related_material:
record:
- id: '1677'
relation: part_of_dissertation
status: public
- id: '550'
relation: part_of_dissertation
status: public
- id: '6183'
relation: part_of_dissertation
status: public
- id: '566'
relation: part_of_dissertation
status: public
- id: '1010'
relation: part_of_dissertation
status: public
- id: '6240'
relation: part_of_dissertation
status: public
- id: '6184'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
title: Dyson equation and eigenvalue statistics of random matrices
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2018'
...
---
_id: '483'
abstract:
- lang: eng
text: We prove the universality for the eigenvalue gap statistics in the bulk of
the spectrum for band matrices, in the regime where the band width is comparable
with the dimension of the matrix, W ~ N. All previous results concerning universality
of non-Gaussian random matrices are for mean-field models. By relying on a new
mean-field reduction technique, we deduce universality from quantum unique ergodicity
for band matrices.
author:
- first_name: Paul
full_name: Bourgade, Paul
last_name: Bourgade
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Horng
full_name: Yau, Horng
last_name: Yau
- first_name: Jun
full_name: Yin, Jun
last_name: Yin
citation:
ama: Bourgade P, Erdös L, Yau H, Yin J. Universality for a class of random band
matrices. Advances in Theoretical and Mathematical Physics. 2017;21(3):739-800.
doi:10.4310/ATMP.2017.v21.n3.a5
apa: Bourgade, P., Erdös, L., Yau, H., & Yin, J. (2017). Universality for a
class of random band matrices. Advances in Theoretical and Mathematical Physics.
International Press. https://doi.org/10.4310/ATMP.2017.v21.n3.a5
chicago: Bourgade, Paul, László Erdös, Horng Yau, and Jun Yin. “Universality for
a Class of Random Band Matrices.” Advances in Theoretical and Mathematical
Physics. International Press, 2017. https://doi.org/10.4310/ATMP.2017.v21.n3.a5.
ieee: P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Universality for a class of random
band matrices,” Advances in Theoretical and Mathematical Physics, vol.
21, no. 3. International Press, pp. 739–800, 2017.
ista: Bourgade P, Erdös L, Yau H, Yin J. 2017. Universality for a class of random
band matrices. Advances in Theoretical and Mathematical Physics. 21(3), 739–800.
mla: Bourgade, Paul, et al. “Universality for a Class of Random Band Matrices.”
Advances in Theoretical and Mathematical Physics, vol. 21, no. 3, International
Press, 2017, pp. 739–800, doi:10.4310/ATMP.2017.v21.n3.a5.
short: P. Bourgade, L. Erdös, H. Yau, J. Yin, Advances in Theoretical and Mathematical
Physics 21 (2017) 739–800.
date_created: 2018-12-11T11:46:43Z
date_published: 2017-08-25T00:00:00Z
date_updated: 2021-01-12T08:00:57Z
day: '25'
department:
- _id: LaEr
doi: 10.4310/ATMP.2017.v21.n3.a5
ec_funded: 1
intvolume: ' 21'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1602.02312
month: '08'
oa: 1
oa_version: Submitted Version
page: 739 - 800
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Advances in Theoretical and Mathematical Physics
publication_identifier:
issn:
- '10950761'
publication_status: published
publisher: International Press
publist_id: '7337'
quality_controlled: '1'
scopus_import: 1
status: public
title: Universality for a class of random band matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 21
year: '2017'
...
---
_id: '567'
abstract:
- lang: eng
text: "This book is a concise and self-contained introduction of recent techniques
to prove local spectral universality for large random matrices. Random matrix
theory is a fast expanding research area, and this book mainly focuses on the
methods that the authors participated in developing over the past few years. Many
other interesting topics are not included, and neither are several new developments
within the framework of these methods. The authors have chosen instead to present
key concepts that they believe are the core of these methods and should be relevant
for future applications. They keep technicalities to a minimum to make the book
accessible to graduate students. With this in mind, they include in this book
the basic notions and tools for high-dimensional analysis, such as large deviation,
entropy, Dirichlet form, and the logarithmic Sobolev inequality.\r\n"
alternative_title:
- Courant Lecture Notes
article_processing_charge: No
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Horng
full_name: Yau, Horng
last_name: Yau
citation:
ama: Erdös L, Yau H. A Dynamical Approach to Random Matrix Theory. Vol 28.
American Mathematical Society; 2017. doi:10.1090/cln/028
apa: Erdös, L., & Yau, H. (2017). A Dynamical Approach to Random Matrix Theory
(Vol. 28). American Mathematical Society. https://doi.org/10.1090/cln/028
chicago: Erdös, László, and Horng Yau. A Dynamical Approach to Random Matrix
Theory. Vol. 28. Courant Lecture Notes. American Mathematical Society, 2017.
https://doi.org/10.1090/cln/028.
ieee: L. Erdös and H. Yau, A Dynamical Approach to Random Matrix Theory,
vol. 28. American Mathematical Society, 2017.
ista: Erdös L, Yau H. 2017. A Dynamical Approach to Random Matrix Theory, American
Mathematical Society, 226p.
mla: Erdös, László, and Horng Yau. A Dynamical Approach to Random Matrix Theory.
Vol. 28, American Mathematical Society, 2017, doi:10.1090/cln/028.
short: L. Erdös, H. Yau, A Dynamical Approach to Random Matrix Theory, American
Mathematical Society, 2017.
date_created: 2018-12-11T11:47:13Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2022-05-24T06:57:28Z
day: '01'
department:
- _id: LaEr
doi: 10.1090/cln/028
ec_funded: 1
intvolume: ' 28'
language:
- iso: eng
month: '01'
oa_version: None
page: '226'
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication_identifier:
eisbn:
- 978-1-4704-4194-4
isbn:
- 9-781-4704-3648-3
publication_status: published
publisher: American Mathematical Society
publist_id: '7247'
quality_controlled: '1'
series_title: Courant Lecture Notes
status: public
title: A Dynamical Approach to Random Matrix Theory
type: book
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2017'
...
---
_id: '615'
abstract:
- lang: eng
text: We show that the Dyson Brownian Motion exhibits local universality after a
very short time assuming that local rigidity and level repulsion of the eigenvalues
hold. These conditions are verified, hence bulk spectral universality is proven,
for a large class of Wigner-like matrices, including deformed Wigner ensembles
and ensembles with non-stochastic variance matrices whose limiting densities differ
from Wigner's semicircle law.
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Kevin
full_name: Schnelli, Kevin
id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
last_name: Schnelli
orcid: 0000-0003-0954-3231
citation:
ama: Erdös L, Schnelli K. Universality for random matrix flows with time dependent
density. Annales de l’institut Henri Poincare (B) Probability and Statistics.
2017;53(4):1606-1656. doi:10.1214/16-AIHP765
apa: Erdös, L., & Schnelli, K. (2017). Universality for random matrix flows
with time dependent density. Annales de l’institut Henri Poincare (B) Probability
and Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/16-AIHP765
chicago: Erdös, László, and Kevin Schnelli. “Universality for Random Matrix Flows
with Time Dependent Density.” Annales de l’institut Henri Poincare (B) Probability
and Statistics. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/16-AIHP765.
ieee: L. Erdös and K. Schnelli, “Universality for random matrix flows with time
dependent density,” Annales de l’institut Henri Poincare (B) Probability and
Statistics, vol. 53, no. 4. Institute of Mathematical Statistics, pp. 1606–1656,
2017.
ista: Erdös L, Schnelli K. 2017. Universality for random matrix flows with time
dependent density. Annales de l’institut Henri Poincare (B) Probability and Statistics.
53(4), 1606–1656.
mla: Erdös, László, and Kevin Schnelli. “Universality for Random Matrix Flows with
Time Dependent Density.” Annales de l’institut Henri Poincare (B) Probability
and Statistics, vol. 53, no. 4, Institute of Mathematical Statistics, 2017,
pp. 1606–56, doi:10.1214/16-AIHP765.
short: L. Erdös, K. Schnelli, Annales de l’institut Henri Poincare (B) Probability
and Statistics 53 (2017) 1606–1656.
date_created: 2018-12-11T11:47:30Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2021-01-12T08:06:22Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/16-AIHP765
ec_funded: 1
intvolume: ' 53'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1504.00650
month: '11'
oa: 1
oa_version: Submitted Version
page: 1606 - 1656
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Annales de l'institut Henri Poincare (B) Probability and Statistics
publication_identifier:
issn:
- '02460203'
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '7189'
quality_controlled: '1'
scopus_import: 1
status: public
title: Universality for random matrix flows with time dependent density
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 53
year: '2017'
...
---
_id: '721'
abstract:
- lang: eng
text: 'Let S be a positivity-preserving symmetric linear operator acting on bounded
functions. The nonlinear equation -1/m=z+Sm with a parameter z in the complex
upper half-plane ℍ has a unique solution m with values in ℍ. We show that the
z-dependence of this solution can be represented as the Stieltjes transforms of
a family of probability measures v on ℝ. Under suitable conditions on S, we show
that v has a real analytic density apart from finitely many algebraic singularities
of degree at most 3. Our motivation comes from large random matrices. The solution
m determines the density of eigenvalues of two prominent matrix ensembles: (i)
matrices with centered independent entries whose variances are given by S and
(ii) matrices with correlated entries with a translation-invariant correlation
structure. Our analysis shows that the limiting eigenvalue density has only square
root singularities or cubic root cusps; no other singularities occur.'
author:
- first_name: Oskari H
full_name: Ajanki, Oskari H
id: 36F2FB7E-F248-11E8-B48F-1D18A9856A87
last_name: Ajanki
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
citation:
ama: Ajanki OH, Krüger TH, Erdös L. Singularities of solutions to quadratic vector
equations on the complex upper half plane. Communications on Pure and Applied
Mathematics. 2017;70(9):1672-1705. doi:10.1002/cpa.21639
apa: Ajanki, O. H., Krüger, T. H., & Erdös, L. (2017). Singularities of solutions
to quadratic vector equations on the complex upper half plane. Communications
on Pure and Applied Mathematics. Wiley-Blackwell. https://doi.org/10.1002/cpa.21639
chicago: Ajanki, Oskari H, Torben H Krüger, and László Erdös. “Singularities of
Solutions to Quadratic Vector Equations on the Complex Upper Half Plane.” Communications
on Pure and Applied Mathematics. Wiley-Blackwell, 2017. https://doi.org/10.1002/cpa.21639.
ieee: O. H. Ajanki, T. H. Krüger, and L. Erdös, “Singularities of solutions to quadratic
vector equations on the complex upper half plane,” Communications on Pure and
Applied Mathematics, vol. 70, no. 9. Wiley-Blackwell, pp. 1672–1705, 2017.
ista: Ajanki OH, Krüger TH, Erdös L. 2017. Singularities of solutions to quadratic
vector equations on the complex upper half plane. Communications on Pure and Applied
Mathematics. 70(9), 1672–1705.
mla: Ajanki, Oskari H., et al. “Singularities of Solutions to Quadratic Vector Equations
on the Complex Upper Half Plane.” Communications on Pure and Applied Mathematics,
vol. 70, no. 9, Wiley-Blackwell, 2017, pp. 1672–705, doi:10.1002/cpa.21639.
short: O.H. Ajanki, T.H. Krüger, L. Erdös, Communications on Pure and Applied Mathematics
70 (2017) 1672–1705.
date_created: 2018-12-11T11:48:08Z
date_published: 2017-09-01T00:00:00Z
date_updated: 2021-01-12T08:12:24Z
day: '01'
department:
- _id: LaEr
doi: 10.1002/cpa.21639
ec_funded: 1
intvolume: ' 70'
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1512.03703
month: '09'
oa: 1
oa_version: Submitted Version
page: 1672 - 1705
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Communications on Pure and Applied Mathematics
publication_identifier:
issn:
- '00103640'
publication_status: published
publisher: Wiley-Blackwell
publist_id: '6959'
quality_controlled: '1'
scopus_import: 1
status: public
title: Singularities of solutions to quadratic vector equations on the complex upper
half plane
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 70
year: '2017'
...
---
_id: '550'
abstract:
- lang: eng
text: For large random matrices X with independent, centered entries but not necessarily
identical variances, the eigenvalue density of XX* is well-approximated by a deterministic
measure on ℝ. We show that the density of this measure has only square and cubic-root
singularities away from zero. We also extend the bulk local law in [5] to the
vicinity of these singularities.
article_number: '63'
author:
- first_name: Johannes
full_name: Alt, Johannes
id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
last_name: Alt
citation:
ama: Alt J. Singularities of the density of states of random Gram matrices. Electronic
Communications in Probability. 2017;22. doi:10.1214/17-ECP97
apa: Alt, J. (2017). Singularities of the density of states of random Gram matrices.
Electronic Communications in Probability. Institute of Mathematical Statistics.
https://doi.org/10.1214/17-ECP97
chicago: Alt, Johannes. “Singularities of the Density of States of Random Gram Matrices.”
Electronic Communications in Probability. Institute of Mathematical Statistics,
2017. https://doi.org/10.1214/17-ECP97.
ieee: J. Alt, “Singularities of the density of states of random Gram matrices,”
Electronic Communications in Probability, vol. 22. Institute of Mathematical
Statistics, 2017.
ista: Alt J. 2017. Singularities of the density of states of random Gram matrices.
Electronic Communications in Probability. 22, 63.
mla: Alt, Johannes. “Singularities of the Density of States of Random Gram Matrices.”
Electronic Communications in Probability, vol. 22, 63, Institute of Mathematical
Statistics, 2017, doi:10.1214/17-ECP97.
short: J. Alt, Electronic Communications in Probability 22 (2017).
date_created: 2018-12-11T11:47:07Z
date_published: 2017-11-21T00:00:00Z
date_updated: 2023-09-07T12:38:08Z
day: '21'
ddc:
- '539'
department:
- _id: LaEr
doi: 10.1214/17-ECP97
ec_funded: 1
file:
- access_level: open_access
checksum: 0ec05303a0de190de145654237984c79
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:08:04Z
date_updated: 2020-07-14T12:47:00Z
file_id: '4663'
file_name: IST-2018-926-v1+1_euclid.ecp.1511233247.pdf
file_size: 470876
relation: main_file
file_date_updated: 2020-07-14T12:47:00Z
has_accepted_license: '1'
intvolume: ' 22'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Electronic Communications in Probability
publication_identifier:
issn:
- 1083589X
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '7265'
pubrep_id: '926'
quality_controlled: '1'
related_material:
record:
- id: '149'
relation: dissertation_contains
status: public
scopus_import: 1
status: public
title: Singularities of the density of states of random Gram matrices
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 22
year: '2017'
...
---
_id: '1144'
abstract:
- lang: eng
text: We show that matrix elements of functions of N × N Wigner matrices fluctuate
on a scale of order N−1/2 and we identify the limiting fluctuation. Our result
holds for any function f of the matrix that has bounded variation thus considerably
relaxing the regularity requirement imposed in [7, 11].
acknowledgement: Partially supported by the IST Austria Excellence Scholarship.
article_number: '86'
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: Erdös L, Schröder DJ. Fluctuations of functions of Wigner matrices. Electronic
Communications in Probability. 2017;21. doi:10.1214/16-ECP38
apa: Erdös, L., & Schröder, D. J. (2017). Fluctuations of functions of Wigner
matrices. Electronic Communications in Probability. Institute of Mathematical
Statistics. https://doi.org/10.1214/16-ECP38
chicago: Erdös, László, and Dominik J Schröder. “Fluctuations of Functions of Wigner
Matrices.” Electronic Communications in Probability. Institute of Mathematical
Statistics, 2017. https://doi.org/10.1214/16-ECP38.
ieee: L. Erdös and D. J. Schröder, “Fluctuations of functions of Wigner matrices,”
Electronic Communications in Probability, vol. 21. Institute of Mathematical
Statistics, 2017.
ista: Erdös L, Schröder DJ. 2017. Fluctuations of functions of Wigner matrices.
Electronic Communications in Probability. 21, 86.
mla: Erdös, László, and Dominik J. Schröder. “Fluctuations of Functions of Wigner
Matrices.” Electronic Communications in Probability, vol. 21, 86, Institute
of Mathematical Statistics, 2017, doi:10.1214/16-ECP38.
short: L. Erdös, D.J. Schröder, Electronic Communications in Probability 21 (2017).
date_created: 2018-12-11T11:50:23Z
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title: Fluctuations of functions of Wigner matrices
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type: journal_article
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---
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abstract:
- lang: eng
text: 'We consider N×N Hermitian random matrices H consisting of blocks of size
M≥N6/7. The matrix elements are i.i.d. within the blocks, close to a Gaussian
in the four moment matching sense, but their distribution varies from block to
block to form a block-band structure, with an essential band width M. We show
that the entries of the Green’s function G(z)=(H−z)−1 satisfy the local semicircle
law with spectral parameter z=E+iη down to the real axis for any η≫N−1, using
a combination of the supersymmetry method inspired by Shcherbina (J Stat Phys
155(3): 466–499, 2014) and the Green’s function comparison strategy. Previous
estimates were valid only for η≫M−1. The new estimate also implies that the eigenvectors
in the middle of the spectrum are fully delocalized.'
acknowledgement: "Z. Bao was supported by ERC Advanced Grant RANMAT No. 338804; L.
Erdős was partially supported by ERC Advanced Grant RANMAT No. 338804.\r\nOpen access
funding provided by Institute of Science and Technology (IST Austria). The authors
are very grateful to the anonymous referees for careful reading and valuable comments,
which helped to improve the organization."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Zhigang
full_name: Bao, Zhigang
id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
last_name: Bao
orcid: 0000-0003-3036-1475
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
citation:
ama: Bao Z, Erdös L. Delocalization for a class of random block band matrices. Probability
Theory and Related Fields. 2017;167(3-4):673-776. doi:10.1007/s00440-015-0692-y
apa: Bao, Z., & Erdös, L. (2017). Delocalization for a class of random block
band matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-015-0692-y
chicago: Bao, Zhigang, and László Erdös. “Delocalization for a Class of Random Block
Band Matrices.” Probability Theory and Related Fields. Springer, 2017.
https://doi.org/10.1007/s00440-015-0692-y.
ieee: Z. Bao and L. Erdös, “Delocalization for a class of random block band matrices,”
Probability Theory and Related Fields, vol. 167, no. 3–4. Springer, pp.
673–776, 2017.
ista: Bao Z, Erdös L. 2017. Delocalization for a class of random block band matrices.
Probability Theory and Related Fields. 167(3–4), 673–776.
mla: Bao, Zhigang, and László Erdös. “Delocalization for a Class of Random Block
Band Matrices.” Probability Theory and Related Fields, vol. 167, no. 3–4,
Springer, 2017, pp. 673–776, doi:10.1007/s00440-015-0692-y.
short: Z. Bao, L. Erdös, Probability Theory and Related Fields 167 (2017) 673–776.
date_created: 2018-12-11T11:52:32Z
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date_updated: 2023-09-20T09:42:12Z
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page: 673 - 776
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call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Probability Theory and Related Fields
publication_identifier:
issn:
- '01788051'
publication_status: published
publisher: Springer
publist_id: '5644'
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title: Delocalization for a class of random block band matrices
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...