---
_id: '12184'
abstract:
- lang: eng
text: We review recent results on adiabatic theory for ground states of extended
gapped fermionic lattice systems under several different assumptions. More precisely,
we present generalized super-adiabatic theorems for extended but finite and infinite
systems, assuming either a uniform gap or a gap in the bulk above the unperturbed
ground state. The goal of this Review is to provide an overview of these adiabatic
theorems and briefly outline the main ideas and techniques required in their proofs.
acknowledgement: "It is a pleasure to thank Stefan Teufel for numerous interesting
discussions, fruitful collaboration, and many helpful comments on an earlier version
of the manuscript. J.H. acknowledges partial financial support from the ERC Advanced
Grant No. 101020331 “Random\r\nmatrices beyond Wigner-Dyson-Mehta.” T.W. acknowledges
financial support from the DFG research unit FOR 5413 “Long-range interacting quantum
spin systems out of equilibrium: Experiment, Theory and Mathematics.\" "
article_number: '121101'
article_processing_charge: No
article_type: original
author:
- first_name: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- first_name: Tom
full_name: Wessel, Tom
last_name: Wessel
citation:
ama: Henheik SJ, Wessel T. On adiabatic theory for extended fermionic lattice systems.
Journal of Mathematical Physics. 2022;63(12). doi:10.1063/5.0123441
apa: Henheik, S. J., & Wessel, T. (2022). On adiabatic theory for extended fermionic
lattice systems. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0123441
chicago: Henheik, Sven Joscha, and Tom Wessel. “On Adiabatic Theory for Extended
Fermionic Lattice Systems.” Journal of Mathematical Physics. AIP Publishing,
2022. https://doi.org/10.1063/5.0123441.
ieee: S. J. Henheik and T. Wessel, “On adiabatic theory for extended fermionic lattice
systems,” Journal of Mathematical Physics, vol. 63, no. 12. AIP Publishing,
2022.
ista: Henheik SJ, Wessel T. 2022. On adiabatic theory for extended fermionic lattice
systems. Journal of Mathematical Physics. 63(12), 121101.
mla: Henheik, Sven Joscha, and Tom Wessel. “On Adiabatic Theory for Extended Fermionic
Lattice Systems.” Journal of Mathematical Physics, vol. 63, no. 12, 121101,
AIP Publishing, 2022, doi:10.1063/5.0123441.
short: S.J. Henheik, T. Wessel, Journal of Mathematical Physics 63 (2022).
date_created: 2023-01-15T23:00:52Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2023-08-04T09:14:57Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1063/5.0123441
ec_funded: 1
external_id:
arxiv:
- '2208.12220'
isi:
- '000905776200001'
file:
- access_level: open_access
checksum: 213b93750080460718c050e4967cfdb4
content_type: application/pdf
creator: dernst
date_created: 2023-01-27T07:10:52Z
date_updated: 2023-01-27T07:10:52Z
file_id: '12410'
file_name: 2022_JourMathPhysics_Henheik2.pdf
file_size: 5251092
relation: main_file
success: 1
file_date_updated: 2023-01-27T07:10:52Z
has_accepted_license: '1'
intvolume: ' 63'
isi: 1
issue: '12'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Journal of Mathematical Physics
publication_identifier:
issn:
- 0022-2488
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: On adiabatic theory for extended fermionic lattice systems
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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 63
year: '2022'
...
---
_id: '12214'
abstract:
- lang: eng
text: 'Motivated by Kloeckner’s result on the isometry group of the quadratic Wasserstein
space W2(Rn), we describe the isometry group Isom(Wp(E)) for all parameters 0
< p < ∞ and for all separable real Hilbert spaces E. In particular, we show that
Wp(X) is isometrically rigid for all Polish space X whenever 0 < p < 1. This is
a consequence of our more general result: we prove that W1(X) is isometrically
rigid if X is a complete separable metric space that satisfies the strict triangle
inequality. Furthermore, we show that this latter rigidity result does not generalise
to parameters p > 1, by solving Kloeckner’s problem affirmatively on the existence
of mass-splitting isometries. '
acknowledgement: "Geher was supported by the Leverhulme Trust Early Career Fellowship
(ECF-2018-125), and also by the Hungarian National Research, Development and Innovation
Office - NKFIH (grant no. K115383 and K134944).\r\nTitkos was supported by the Hungarian
National Research, Development and Innovation Office - NKFIH (grant no. PD128374,
grant no. K115383 and K134944), by the J´anos Bolyai Research Scholarship of the
Hungarian Academy of Sciences, and by the UNKP-20-5-BGE-1 New National Excellence
Program of the ´Ministry of Innovation and Technology.\r\nVirosztek was supported
by the European Union’s Horizon 2020 research and innovation program under the Marie
Sklodowska-Curie Grant Agreement No. 846294, by the Momentum program of the Hungarian
Academy of Sciences under grant agreement no. LP2021-15/2021, and partially supported
by the Hungarian National Research, Development and Innovation Office - NKFIH (grants
no. K124152 and no. KH129601). "
article_processing_charge: No
article_type: original
author:
- first_name: György Pál
full_name: Gehér, György Pál
last_name: Gehér
- first_name: Tamás
full_name: Titkos, Tamás
last_name: Titkos
- first_name: Daniel
full_name: Virosztek, Daniel
id: 48DB45DA-F248-11E8-B48F-1D18A9856A87
last_name: Virosztek
orcid: 0000-0003-1109-5511
citation:
ama: 'Gehér GP, Titkos T, Virosztek D. The isometry group of Wasserstein spaces:
The Hilbertian case. Journal of the London Mathematical Society. 2022;106(4):3865-3894.
doi:10.1112/jlms.12676'
apa: 'Gehér, G. P., Titkos, T., & Virosztek, D. (2022). The isometry group of
Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical
Society. Wiley. https://doi.org/10.1112/jlms.12676'
chicago: 'Gehér, György Pál, Tamás Titkos, and Daniel Virosztek. “The Isometry Group
of Wasserstein Spaces: The Hilbertian Case.” Journal of the London Mathematical
Society. Wiley, 2022. https://doi.org/10.1112/jlms.12676.'
ieee: 'G. P. Gehér, T. Titkos, and D. Virosztek, “The isometry group of Wasserstein
spaces: The Hilbertian case,” Journal of the London Mathematical Society,
vol. 106, no. 4. Wiley, pp. 3865–3894, 2022.'
ista: 'Gehér GP, Titkos T, Virosztek D. 2022. The isometry group of Wasserstein
spaces: The Hilbertian case. Journal of the London Mathematical Society. 106(4),
3865–3894.'
mla: 'Gehér, György Pál, et al. “The Isometry Group of Wasserstein Spaces: The Hilbertian
Case.” Journal of the London Mathematical Society, vol. 106, no. 4, Wiley,
2022, pp. 3865–94, doi:10.1112/jlms.12676.'
short: G.P. Gehér, T. Titkos, D. Virosztek, Journal of the London Mathematical Society
106 (2022) 3865–3894.
date_created: 2023-01-16T09:46:13Z
date_published: 2022-09-18T00:00:00Z
date_updated: 2023-08-04T09:24:17Z
day: '18'
department:
- _id: LaEr
doi: 10.1112/jlms.12676
ec_funded: 1
external_id:
arxiv:
- '2102.02037'
isi:
- '000854878500001'
intvolume: ' 106'
isi: 1
issue: '4'
keyword:
- General Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2102.02037
month: '09'
oa: 1
oa_version: Preprint
page: 3865-3894
project:
- _id: 26A455A6-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '846294'
name: Geometric study of Wasserstein spaces and free probability
publication: Journal of the London Mathematical Society
publication_identifier:
eissn:
- 1469-7750
issn:
- 0024-6107
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'The isometry group of Wasserstein spaces: The Hilbertian case'
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 106
year: '2022'
...
---
_id: '12232'
abstract:
- lang: eng
text: We derive a precise asymptotic formula for the density of the small singular
values of the real Ginibre matrix ensemble shifted by a complex parameter z as
the dimension tends to infinity. For z away from the real axis the formula coincides
with that for the complex Ginibre ensemble we derived earlier in Cipolloni et
al. (Prob Math Phys 1:101–146, 2020). On the level of the one-point function of
the low lying singular values we thus confirm the transition from real to complex
Ginibre ensembles as the shift parameter z becomes genuinely complex; the analogous
phenomenon has been well known for eigenvalues. We use the superbosonization formula
(Littelmann et al. in Comm Math Phys 283:343–395, 2008) in a regime where the
main contribution comes from a three dimensional saddle manifold.
acknowledgement: Open access funding provided by Swiss Federal Institute of Technology
Zurich. Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH
Zürich Foundation.
article_processing_charge: No
article_type: original
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- 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: Cipolloni G, Erdös L, Schröder DJ. Density of small singular values of the
shifted real Ginibre ensemble. Annales Henri Poincaré. 2022;23(11):3981-4002.
doi:10.1007/s00023-022-01188-8
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Density of small singular
values of the shifted real Ginibre ensemble. Annales Henri Poincaré. Springer
Nature. https://doi.org/10.1007/s00023-022-01188-8
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Density of Small
Singular Values of the Shifted Real Ginibre Ensemble.” Annales Henri Poincaré.
Springer Nature, 2022. https://doi.org/10.1007/s00023-022-01188-8.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Density of small singular values
of the shifted real Ginibre ensemble,” Annales Henri Poincaré, vol. 23,
no. 11. Springer Nature, pp. 3981–4002, 2022.
ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Density of small singular values
of the shifted real Ginibre ensemble. Annales Henri Poincaré. 23(11), 3981–4002.
mla: Cipolloni, Giorgio, et al. “Density of Small Singular Values of the Shifted
Real Ginibre Ensemble.” Annales Henri Poincaré, vol. 23, no. 11, Springer
Nature, 2022, pp. 3981–4002, doi:10.1007/s00023-022-01188-8.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002.
date_created: 2023-01-16T09:50:26Z
date_published: 2022-11-01T00:00:00Z
date_updated: 2023-08-04T09:33:52Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00023-022-01188-8
external_id:
isi:
- '000796323500001'
file:
- access_level: open_access
checksum: 5582f059feeb2f63e2eb68197a34d7dc
content_type: application/pdf
creator: dernst
date_created: 2023-01-27T11:06:47Z
date_updated: 2023-01-27T11:06:47Z
file_id: '12424'
file_name: 2022_AnnalesHenriP_Cipolloni.pdf
file_size: 1333638
relation: main_file
success: 1
file_date_updated: 2023-01-27T11:06:47Z
has_accepted_license: '1'
intvolume: ' 23'
isi: 1
issue: '11'
keyword:
- Mathematical Physics
- Nuclear and High Energy Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 3981-4002
publication: Annales Henri Poincaré
publication_identifier:
eissn:
- 1424-0661
issn:
- 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Density of small singular values of the shifted real Ginibre ensemble
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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 23
year: '2022'
...
---
_id: '12243'
abstract:
- lang: eng
text: 'We consider the eigenvalues of a large dimensional real or complex Ginibre
matrix in the region of the complex plane where their real parts reach their maximum
value. This maximum follows the Gumbel distribution and that these extreme eigenvalues
form a Poisson point process as the dimension asymptotically tends to infinity.
In the complex case, these facts have already been established by Bender [Probab.
Theory Relat. Fields 147, 241 (2010)] and in the real case by Akemann and Phillips
[J. Stat. Phys. 155, 421 (2014)] even for the more general elliptic ensemble with
a sophisticated saddle point analysis. The purpose of this article is to give
a very short direct proof in the Ginibre case with an effective error term. Moreover,
our estimates on the correlation kernel in this regime serve as a key input for
accurately locating [Formula: see text] for any large matrix X with i.i.d. entries
in the companion paper [G. Cipolloni et al., arXiv:2206.04448 (2022)]. '
acknowledgement: "The authors are grateful to G. Akemann for bringing Refs. 19 and
24–26 to their attention. Discussions with Guillaume Dubach on a preliminary version
of this project are acknowledged.\r\nL.E. and Y.X. were supported by the ERC Advanced
Grant “RMTBeyond” under Grant No. 101020331. D.S. was supported by Dr. Max Rössler,
the Walter Haefner Foundation, and the ETH Zürich Foundation."
article_number: '103303'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- 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
- first_name: Yuanyuan
full_name: Xu, Yuanyuan
id: 7902bdb1-a2a4-11eb-a164-c9216f71aea3
last_name: Xu
citation:
ama: Cipolloni G, Erdös L, Schröder DJ, Xu Y. Directional extremal statistics for
Ginibre eigenvalues. Journal of Mathematical Physics. 2022;63(10). doi:10.1063/5.0104290
apa: Cipolloni, G., Erdös, L., Schröder, D. J., & Xu, Y. (2022). Directional
extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics.
AIP Publishing. https://doi.org/10.1063/5.0104290
chicago: Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu.
“Directional Extremal Statistics for Ginibre Eigenvalues.” Journal of Mathematical
Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0104290.
ieee: G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “Directional extremal statistics
for Ginibre eigenvalues,” Journal of Mathematical Physics, vol. 63, no.
10. AIP Publishing, 2022.
ista: Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2022. Directional extremal statistics
for Ginibre eigenvalues. Journal of Mathematical Physics. 63(10), 103303.
mla: Cipolloni, Giorgio, et al. “Directional Extremal Statistics for Ginibre Eigenvalues.”
Journal of Mathematical Physics, vol. 63, no. 10, 103303, AIP Publishing,
2022, doi:10.1063/5.0104290.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, Journal of Mathematical Physics
63 (2022).
date_created: 2023-01-16T09:52:58Z
date_published: 2022-10-14T00:00:00Z
date_updated: 2023-08-04T09:40:02Z
day: '14'
ddc:
- '510'
- '530'
department:
- _id: LaEr
doi: 10.1063/5.0104290
ec_funded: 1
external_id:
arxiv:
- '2206.04443'
isi:
- '000869715800001'
file:
- access_level: open_access
checksum: 2db278ae5b07f345a7e3fec1f92b5c33
content_type: application/pdf
creator: dernst
date_created: 2023-01-30T08:01:10Z
date_updated: 2023-01-30T08:01:10Z
file_id: '12436'
file_name: 2022_JourMathPhysics_Cipolloni2.pdf
file_size: 7356807
relation: main_file
success: 1
file_date_updated: 2023-01-30T08:01:10Z
has_accepted_license: '1'
intvolume: ' 63'
isi: 1
issue: '10'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Journal of Mathematical Physics
publication_identifier:
eissn:
- 1089-7658
issn:
- 0022-2488
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Directional extremal statistics for Ginibre eigenvalues
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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 63
year: '2022'
...
---
_id: '12290'
abstract:
- lang: eng
text: We prove local laws, i.e. optimal concentration estimates for arbitrary products
of resolvents of a Wigner random matrix with deterministic matrices in between.
We find that the size of such products heavily depends on whether some of the
deterministic matrices are traceless. Our estimates correctly account for this
dependence and they hold optimally down to the smallest possible spectral scale.
acknowledgement: L. Erdős was supported by ERC Advanced Grant “RMTBeyond” No. 101020331.
D. Schröder was supported by Dr. Max Rössler, the Walter Haefner Foundation and
the ETH Zürich Foundation.
article_processing_charge: No
article_type: original
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- 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: Cipolloni G, Erdös L, Schröder DJ. Optimal multi-resolvent local laws for Wigner
matrices. Electronic Journal of Probability. 2022;27:1-38. doi:10.1214/22-ejp838
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Optimal multi-resolvent
local laws for Wigner matrices. Electronic Journal of Probability. Institute
of Mathematical Statistics. https://doi.org/10.1214/22-ejp838
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Multi-Resolvent
Local Laws for Wigner Matrices.” Electronic Journal of Probability. Institute
of Mathematical Statistics, 2022. https://doi.org/10.1214/22-ejp838.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal multi-resolvent local
laws for Wigner matrices,” Electronic Journal of Probability, vol. 27.
Institute of Mathematical Statistics, pp. 1–38, 2022.
ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws
for Wigner matrices. Electronic Journal of Probability. 27, 1–38.
mla: Cipolloni, Giorgio, et al. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.”
Electronic Journal of Probability, vol. 27, Institute of Mathematical Statistics,
2022, pp. 1–38, doi:10.1214/22-ejp838.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability
27 (2022) 1–38.
date_created: 2023-01-16T10:04:38Z
date_published: 2022-09-12T00:00:00Z
date_updated: 2023-08-04T10:32:23Z
day: '12'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1214/22-ejp838
ec_funded: 1
external_id:
isi:
- '000910863700003'
file:
- access_level: open_access
checksum: bb647b48fbdb59361210e425c220cdcb
content_type: application/pdf
creator: dernst
date_created: 2023-01-30T11:59:21Z
date_updated: 2023-01-30T11:59:21Z
file_id: '12464'
file_name: 2022_ElecJournProbability_Cipolloni.pdf
file_size: 502149
relation: main_file
success: 1
file_date_updated: 2023-01-30T11:59:21Z
has_accepted_license: '1'
intvolume: ' 27'
isi: 1
keyword:
- Statistics
- Probability and Uncertainty
- Statistics and Probability
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 1-38
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Electronic Journal of Probability
publication_identifier:
eissn:
- 1083-6489
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal multi-resolvent local laws for Wigner 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 27
year: '2022'
...
---
_id: '11732'
abstract:
- lang: eng
text: We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic
formula, which strongly depends on the strength of the interaction potential V
on the Fermi surface. In combination with the recent result by one of us (Math.
Phys. Anal. Geom. 25, 3, 2022) on the critical temperature Tc at high densities,
we prove the universality of the ratio of the energy gap and the critical temperature.
acknowledgement: "We are grateful to Robert Seiringer for helpful discussions and
many valuable comments\r\non an earlier version of the manuscript. J.H. acknowledges
partial financial support by the ERC Advanced Grant “RMTBeyond’ No. 101020331. Open
access funding provided by Institute of Science and Technology (IST Austria)"
article_number: '5'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- first_name: Asbjørn Bækgaard
full_name: Lauritsen, Asbjørn Bækgaard
id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1
last_name: Lauritsen
orcid: 0000-0003-4476-2288
citation:
ama: Henheik SJ, Lauritsen AB. The BCS energy gap at high density. Journal of
Statistical Physics. 2022;189. doi:10.1007/s10955-022-02965-9
apa: Henheik, S. J., & Lauritsen, A. B. (2022). The BCS energy gap at high density.
Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02965-9
chicago: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap
at High Density.” Journal of Statistical Physics. Springer Nature, 2022.
https://doi.org/10.1007/s10955-022-02965-9.
ieee: S. J. Henheik and A. B. Lauritsen, “The BCS energy gap at high density,” Journal
of Statistical Physics, vol. 189. Springer Nature, 2022.
ista: Henheik SJ, Lauritsen AB. 2022. The BCS energy gap at high density. Journal
of Statistical Physics. 189, 5.
mla: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at
High Density.” Journal of Statistical Physics, vol. 189, 5, Springer Nature,
2022, doi:10.1007/s10955-022-02965-9.
short: S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022).
date_created: 2022-08-05T11:36:56Z
date_published: 2022-07-29T00:00:00Z
date_updated: 2023-09-05T14:57:49Z
day: '29'
ddc:
- '530'
department:
- _id: GradSch
- _id: LaEr
- _id: RoSe
doi: 10.1007/s10955-022-02965-9
ec_funded: 1
external_id:
isi:
- '000833007200002'
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creator: dernst
date_created: 2022-08-08T07:36:34Z
date_updated: 2022-08-08T07:36:34Z
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file_name: 2022_JourStatisticalPhysics_Henheik.pdf
file_size: 419563
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file_date_updated: 2022-08-08T07:36:34Z
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intvolume: ' 189'
isi: 1
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Journal of Statistical Physics
publication_identifier:
eissn:
- 1572-9613
issn:
- 0022-4715
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The BCS energy gap at high density
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 189
year: '2022'
...
---
_id: '10285'
abstract:
- lang: eng
text: We study the overlaps between right and left eigenvectors for random matrices
of the spherical ensemble, as well as truncated unitary ensembles in the regime
where half of the matrix at least is truncated. These two integrable models exhibit
a form of duality, and the essential steps of our investigation can therefore
be performed in parallel. In every case, conditionally on all eigenvalues, diagonal
overlaps are shown to be distributed as a product of independent random variables
with explicit distributions. This enables us to prove that the scaled diagonal
overlaps, conditionally on one eigenvalue, converge in distribution to a heavy-tail
limit, namely, the inverse of a γ2 distribution. We also provide formulae for
the conditional expectation of diagonal and off-diagonal overlaps, either with
respect to one eigenvalue, or with respect to the whole spectrum. These results,
analogous to what is known for the complex Ginibre ensemble, can be obtained in
these cases thanks to integration techniques inspired from a previous work by
Forrester & Krishnapur.
acknowledgement: We acknowledge partial support from the grants NSF DMS-1812114 of
P. Bourgade (PI) and NSF CAREER DMS-1653602 of L.-P. Arguin (PI). This project has
also received funding from the European Union’s Horizon 2020 research and innovation
programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. We would
like to thank Paul Bourgade and László Erdős for many helpful comments.
article_number: '124'
article_processing_charge: No
article_type: original
author:
- first_name: Guillaume
full_name: Dubach, Guillaume
id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E
last_name: Dubach
orcid: 0000-0001-6892-8137
citation:
ama: Dubach G. On eigenvector statistics in the spherical and truncated unitary
ensembles. Electronic Journal of Probability. 2021;26. doi:10.1214/21-EJP686
apa: Dubach, G. (2021). On eigenvector statistics in the spherical and truncated
unitary ensembles. Electronic Journal of Probability. Institute of Mathematical
Statistics. https://doi.org/10.1214/21-EJP686
chicago: Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated
Unitary Ensembles.” Electronic Journal of Probability. Institute of Mathematical
Statistics, 2021. https://doi.org/10.1214/21-EJP686.
ieee: G. Dubach, “On eigenvector statistics in the spherical and truncated unitary
ensembles,” Electronic Journal of Probability, vol. 26. Institute of Mathematical
Statistics, 2021.
ista: Dubach G. 2021. On eigenvector statistics in the spherical and truncated unitary
ensembles. Electronic Journal of Probability. 26, 124.
mla: Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated
Unitary Ensembles.” Electronic Journal of Probability, vol. 26, 124, Institute
of Mathematical Statistics, 2021, doi:10.1214/21-EJP686.
short: G. Dubach, Electronic Journal of Probability 26 (2021).
date_created: 2021-11-14T23:01:25Z
date_published: 2021-09-28T00:00:00Z
date_updated: 2021-11-15T10:48:46Z
day: '28'
ddc:
- '519'
department:
- _id: LaEr
doi: 10.1214/21-EJP686
ec_funded: 1
file:
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checksum: 1c975afb31460277ce4d22b93538e5f9
content_type: application/pdf
creator: cchlebak
date_created: 2021-11-15T10:10:17Z
date_updated: 2021-11-15T10:10:17Z
file_id: '10288'
file_name: 2021_ElecJournalProb_Dubach.pdf
file_size: 735940
relation: main_file
success: 1
file_date_updated: 2021-11-15T10:10:17Z
has_accepted_license: '1'
intvolume: ' 26'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Electronic Journal of Probability
publication_identifier:
eissn:
- 1083-6489
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: On eigenvector statistics in the spherical and truncated unitary ensembles
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: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 26
year: '2021'
...
---
_id: '9230'
abstract:
- lang: eng
text: "We consider a model of the Riemann zeta function on the critical axis and
study its maximum over intervals of length (log T)θ, where θ is either fixed or
tends to zero at a suitable rate.\r\nIt is shown that the deterministic level
of the maximum interpolates smoothly between the ones\r\nof log-correlated variables
and of i.i.d. random variables, exhibiting a smooth transition ‘from\r\n3/4 to
1/4’ in the second order. This provides a natural context where extreme value
statistics of\r\nlog-correlated variables with time-dependent variance and rate
occur. A key ingredient of the\r\nproof is a precise upper tail tightness estimate
for the maximum of the model on intervals of\r\nsize one, that includes a Gaussian
correction. This correction is expected to be present for the\r\nRiemann zeta
function and pertains to the question of the correct order of the maximum of\r\nthe
zeta function in large intervals."
acknowledgement: The research of L.-P. A. is supported in part by the grant NSF CAREER
DMS-1653602. G. D. gratefully acknowledges support from the European Union’s Horizon
2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement
No. 754411. The research of L. H. is supported in part by the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation) through Project-ID 233630050 -TRR 146, Project-ID
443891315 within SPP 2265 and Project-ID 446173099.
article_number: '2103.04817'
article_processing_charge: No
author:
- first_name: Louis-Pierre
full_name: Arguin, Louis-Pierre
last_name: Arguin
- first_name: Guillaume
full_name: Dubach, Guillaume
id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E
last_name: Dubach
orcid: 0000-0001-6892-8137
- first_name: Lisa
full_name: Hartung, Lisa
last_name: Hartung
citation:
ama: Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta
function over intervals of varying length. arXiv. doi:10.48550/arXiv.2103.04817
apa: Arguin, L.-P., Dubach, G., & Hartung, L. (n.d.). Maxima of a random model
of the Riemann zeta function over intervals of varying length. arXiv. https://doi.org/10.48550/arXiv.2103.04817
chicago: Arguin, Louis-Pierre, Guillaume Dubach, and Lisa Hartung. “Maxima of a
Random Model of the Riemann Zeta Function over Intervals of Varying Length.” ArXiv,
n.d. https://doi.org/10.48550/arXiv.2103.04817.
ieee: L.-P. Arguin, G. Dubach, and L. Hartung, “Maxima of a random model of the
Riemann zeta function over intervals of varying length,” arXiv. .
ista: Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta
function over intervals of varying length. arXiv, 2103.04817.
mla: Arguin, Louis-Pierre, et al. “Maxima of a Random Model of the Riemann Zeta
Function over Intervals of Varying Length.” ArXiv, 2103.04817, doi:10.48550/arXiv.2103.04817.
short: L.-P. Arguin, G. Dubach, L. Hartung, ArXiv (n.d.).
date_created: 2021-03-09T11:08:15Z
date_published: 2021-03-08T00:00:00Z
date_updated: 2023-05-03T10:22:59Z
day: '08'
department:
- _id: LaEr
doi: 10.48550/arXiv.2103.04817
ec_funded: 1
external_id:
arxiv:
- '2103.04817'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2103.04817
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: arXiv
publication_status: submitted
status: public
title: Maxima of a random model of the Riemann zeta function over intervals of varying
length
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '9281'
abstract:
- lang: eng
text: We comment on two formal proofs of Fermat's sum of two squares theorem, written
using the Mathematical Components libraries of the Coq proof assistant. The first
one follows Zagier's celebrated one-sentence proof; the second follows David Christopher's
recent new proof relying on partition-theoretic arguments. Both formal proofs
rely on a general property of involutions of finite sets, of independent interest.
The proof technique consists for the most part of automating recurrent tasks (such
as case distinctions and computations on natural numbers) via ad hoc tactics.
article_number: '2103.11389'
article_processing_charge: No
author:
- first_name: Guillaume
full_name: Dubach, Guillaume
id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E
last_name: Dubach
orcid: 0000-0001-6892-8137
- first_name: Fabian
full_name: Mühlböck, Fabian
id: 6395C5F6-89DF-11E9-9C97-6BDFE5697425
last_name: Mühlböck
orcid: 0000-0003-1548-0177
citation:
ama: Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. arXiv.
doi:10.48550/arXiv.2103.11389
apa: Dubach, G., & Mühlböck, F. (n.d.). Formal verification of Zagier’s one-sentence
proof. arXiv. https://doi.org/10.48550/arXiv.2103.11389
chicago: Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s
One-Sentence Proof.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2103.11389.
ieee: G. Dubach and F. Mühlböck, “Formal verification of Zagier’s one-sentence proof,”
arXiv. .
ista: Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof.
arXiv, 2103.11389.
mla: Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence
Proof.” ArXiv, 2103.11389, doi:10.48550/arXiv.2103.11389.
short: G. Dubach, F. Mühlböck, ArXiv (n.d.).
date_created: 2021-03-23T05:38:48Z
date_published: 2021-03-21T00:00:00Z
date_updated: 2023-05-03T10:26:45Z
day: '21'
department:
- _id: LaEr
- _id: ToHe
doi: 10.48550/arXiv.2103.11389
ec_funded: 1
external_id:
arxiv:
- '2103.11389'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2103.11389
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: arXiv
publication_status: submitted
related_material:
record:
- id: '9946'
relation: other
status: public
status: public
title: Formal verification of Zagier's one-sentence proof
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '8373'
abstract:
- lang: eng
text: It is well known that special Kubo-Ando operator means admit divergence center
interpretations, moreover, they are also mean squared error estimators for certain
metrics on positive definite operators. In this paper we give a divergence center
interpretation for every symmetric Kubo-Ando mean. This characterization of the
symmetric means naturally leads to a definition of weighted and multivariate versions
of a large class of symmetric Kubo-Ando means. We study elementary properties
of these weighted multivariate means, and note in particular that in the special
case of the geometric mean we recover the weighted A#H-mean introduced by Kim,
Lawson, and Lim.
acknowledgement: "The authors are grateful to Milán Mosonyi for fruitful discussions
on the topic, and to the anonymous referee for his/her comments and suggestions.\r\nJ.
Pitrik was supported by the Hungarian Academy of Sciences Lendület-Momentum Grant
for Quantum Information Theory, No. 96 141, and by Hungarian National Research,
Development and Innovation Office (NKFIH) via grants no. K119442, no. K124152, and
no. KH129601. D. Virosztek was supported by the ISTFELLOW program of the Institute
of Science and Technology Austria (project code IC1027FELL01), by the European Union's
Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant
Agreement No. 846294, and partially supported by the Hungarian National Research,
Development and Innovation Office (NKFIH) via grants no. K124152, and no. KH129601."
article_processing_charge: No
article_type: original
author:
- first_name: József
full_name: Pitrik, József
last_name: Pitrik
- first_name: Daniel
full_name: Virosztek, Daniel
id: 48DB45DA-F248-11E8-B48F-1D18A9856A87
last_name: Virosztek
orcid: 0000-0003-1109-5511
citation:
ama: Pitrik J, Virosztek D. A divergence center interpretation of general symmetric
Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra
and its Applications. 2021;609:203-217. doi:10.1016/j.laa.2020.09.007
apa: Pitrik, J., & Virosztek, D. (2021). A divergence center interpretation
of general symmetric Kubo-Ando means, and related weighted multivariate operator
means. Linear Algebra and Its Applications. Elsevier. https://doi.org/10.1016/j.laa.2020.09.007
chicago: Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation
of General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator
Means.” Linear Algebra and Its Applications. Elsevier, 2021. https://doi.org/10.1016/j.laa.2020.09.007.
ieee: J. Pitrik and D. Virosztek, “A divergence center interpretation of general
symmetric Kubo-Ando means, and related weighted multivariate operator means,”
Linear Algebra and its Applications, vol. 609. Elsevier, pp. 203–217, 2021.
ista: Pitrik J, Virosztek D. 2021. A divergence center interpretation of general
symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear
Algebra and its Applications. 609, 203–217.
mla: Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation of
General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator
Means.” Linear Algebra and Its Applications, vol. 609, Elsevier, 2021,
pp. 203–17, doi:10.1016/j.laa.2020.09.007.
short: J. Pitrik, D. Virosztek, Linear Algebra and Its Applications 609 (2021) 203–217.
date_created: 2020-09-11T08:35:50Z
date_published: 2021-01-15T00:00:00Z
date_updated: 2023-08-04T10:58:14Z
day: '15'
department:
- _id: LaEr
doi: 10.1016/j.laa.2020.09.007
ec_funded: 1
external_id:
arxiv:
- '2002.11678'
isi:
- '000581730500011'
intvolume: ' 609'
isi: 1
keyword:
- Kubo-Ando mean
- weighted multivariate mean
- barycenter
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2002.11678
month: '01'
oa: 1
oa_version: Preprint
page: 203-217
project:
- _id: 26A455A6-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '846294'
name: Geometric study of Wasserstein spaces and free probability
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Linear Algebra and its Applications
publication_identifier:
issn:
- 0024-3795
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: A divergence center interpretation of general symmetric Kubo-Ando means, and
related weighted multivariate operator means
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 609
year: '2021'
...