---
_id: '14667'
abstract:
- lang: eng
text: 'For large dimensional non-Hermitian random matrices X with real or complex
independent, identically distributed, centered entries, we consider the fluctuations
of f (X) as a matrix where f is an analytic function around the spectrum of X.
We prove that for a generic bounded square matrix A, the quantity Tr f (X)A exhibits
Gaussian fluctuations as the matrix size grows to infinity, which consists of
two independent modes corresponding to the tracial and traceless parts of A. We
find a new formula for the variance of the traceless part that involves the Frobenius
norm of A and the L2-norm of f on the boundary of the limiting spectrum. '
- lang: fre
text: On étudie les fluctuations de f (X), où X est une matrice aléatoire non-hermitienne
de grande taille à coefficients i.i.d. (réels ou complexes), et f une fonction
analytique sur un domaine qui contient le spectre de X. On prouve que, pour une
matrice carrée générique et bornée A, les fluctuations de la quantité tr f (X)A
sont asymptotiquement gaussiennes et comportent deux modes indépendants, correspondant
aux composantes traciale et de trace nulle de A. Une nouvelle formule est établie
pour la variance de la composante de trace nulle, qui fait intervenir la norme
de Frobenius de A et la norme L2 de f sur la frontière du spectre limite.
acknowledgement: "The first author was partially supported by ERC Advanced Grant “RMTBeyond”
No. 101020331. The second author was supported by ERC Advanced Grant “RMTBeyond”
No. 101020331.\r\nThe authors are grateful to the anonymous referees and associated
editor for carefully reading this paper and providing helpful comments that improved
the quality of the article. Also the authors would like to thank Peter Forrester
for pointing out the reference [12] that was absent in the previous version of the
manuscript."
article_processing_charge: No
article_type: original
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Hong Chang
full_name: Ji, Hong Chang
id: dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d
last_name: Ji
citation:
ama: Erdös L, Ji HC. Functional CLT for non-Hermitian random matrices. Annales
de l’institut Henri Poincare (B) Probability and Statistics. 2023;59(4):2083-2105.
doi:10.1214/22-AIHP1304
apa: Erdös, L., & Ji, H. C. (2023). Functional CLT for non-Hermitian random
matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics.
Institute of Mathematical Statistics. https://doi.org/10.1214/22-AIHP1304
chicago: Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random
Matrices.” Annales de l’institut Henri Poincare (B) Probability and Statistics.
Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/22-AIHP1304.
ieee: L. Erdös and H. C. Ji, “Functional CLT for non-Hermitian random matrices,”
Annales de l’institut Henri Poincare (B) Probability and Statistics, vol.
59, no. 4. Institute of Mathematical Statistics, pp. 2083–2105, 2023.
ista: Erdös L, Ji HC. 2023. Functional CLT for non-Hermitian random matrices. Annales
de l’institut Henri Poincare (B) Probability and Statistics. 59(4), 2083–2105.
mla: Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random
Matrices.” Annales de l’institut Henri Poincare (B) Probability and Statistics,
vol. 59, no. 4, Institute of Mathematical Statistics, 2023, pp. 2083–105, doi:10.1214/22-AIHP1304.
short: L. Erdös, H.C. Ji, Annales de l’institut Henri Poincare (B) Probability and
Statistics 59 (2023) 2083–2105.
date_created: 2023-12-10T23:01:00Z
date_published: 2023-11-01T00:00:00Z
date_updated: 2023-12-11T12:36:56Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/22-AIHP1304
ec_funded: 1
external_id:
arxiv:
- '2112.11382'
intvolume: ' 59'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2112.11382
month: '11'
oa: 1
oa_version: Preprint
page: 2083-2105
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
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: Functional CLT for non-Hermitian random matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 59
year: '2023'
...
---
_id: '14750'
abstract:
- lang: eng
text: "Consider the random matrix model A1/2UBU∗A1/2, where A and B are two N ×
N deterministic matrices and U is either an N × N Haar unitary or orthogonal random
matrix. It is well known that on the macroscopic scale (Invent. Math. 104 (1991)
201–220), the limiting empirical spectral distribution (ESD) of the above model
is given by the free multiplicative convolution\r\nof the limiting ESDs of A and
B, denoted as μα \x02 μβ, where μα and μβ are the limiting ESDs of A and B, respectively.
In this paper, we study the asymptotic microscopic behavior of the edge eigenvalues
and eigenvectors statistics. We prove that both the density of μA \x02μB, where
μA and μB are the ESDs of A and B, respectively and the associated subordination
functions\r\nhave a regular behavior near the edges. Moreover, we establish the
local laws near the edges on the optimal scale. In particular, we prove that the
entries of the resolvent are close to some functionals depending only on the eigenvalues
of A, B and the subordination functions with optimal convergence rates. Our proofs
and calculations are based on the techniques developed for the additive model
A+UBU∗ in (J. Funct. Anal. 271 (2016) 672–719; Comm. Math.\r\nPhys. 349 (2017)
947–990; Adv. Math. 319 (2017) 251–291; J. Funct. Anal. 279 (2020) 108639), and
our results can be regarded as the counterparts of (J. Funct. Anal. 279 (2020)
108639) for the multiplicative model. "
acknowledgement: "The first author is partially supported by NSF Grant DMS-2113489
and grateful for the AMS-SIMONS travel grant (2020–2023). The second author is supported
by the ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nThe authors would like to
thank the Editor, Associate Editor and an anonymous referee for their many critical
suggestions which have significantly improved the paper. We also want to thank Zhigang
Bao and Ji Oon Lee for many helpful discussions and comments."
article_processing_charge: No
article_type: original
author:
- first_name: Xiucai
full_name: Ding, Xiucai
last_name: Ding
- first_name: Hong Chang
full_name: Ji, Hong Chang
id: dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d
last_name: Ji
citation:
ama: Ding X, Ji HC. Local laws for multiplication of random matrices. The Annals
of Applied Probability. 2023;33(4):2981-3009. doi:10.1214/22-aap1882
apa: Ding, X., & Ji, H. C. (2023). Local laws for multiplication of random matrices.
The Annals of Applied Probability. Institute of Mathematical Statistics.
https://doi.org/10.1214/22-aap1882
chicago: Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random
Matrices.” The Annals of Applied Probability. Institute of Mathematical
Statistics, 2023. https://doi.org/10.1214/22-aap1882.
ieee: X. Ding and H. C. Ji, “Local laws for multiplication of random matrices,”
The Annals of Applied Probability, vol. 33, no. 4. Institute of Mathematical
Statistics, pp. 2981–3009, 2023.
ista: Ding X, Ji HC. 2023. Local laws for multiplication of random matrices. The
Annals of Applied Probability. 33(4), 2981–3009.
mla: Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random Matrices.”
The Annals of Applied Probability, vol. 33, no. 4, Institute of Mathematical
Statistics, 2023, pp. 2981–3009, doi:10.1214/22-aap1882.
short: X. Ding, H.C. Ji, The Annals of Applied Probability 33 (2023) 2981–3009.
date_created: 2024-01-08T13:03:18Z
date_published: 2023-08-01T00:00:00Z
date_updated: 2024-01-09T08:16:41Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/22-aap1882
ec_funded: 1
external_id:
arxiv:
- '2010.16083'
intvolume: ' 33'
issue: '4'
keyword:
- Statistics
- Probability and Uncertainty
- Statistics and Probability
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2010.16083
month: '08'
oa: 1
oa_version: Preprint
page: 2981-3009
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: The Annals of Applied Probability
publication_identifier:
issn:
- 1050-5164
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local laws for multiplication of random matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 33
year: '2023'
...
---
_id: '14780'
abstract:
- lang: eng
text: In this paper, we study the eigenvalues and eigenvectors of the spiked invariant
multiplicative models when the randomness is from Haar matrices. We establish
the limits of the outlier eigenvalues λˆi and the generalized components (⟨v,uˆi⟩
for any deterministic vector v) of the outlier eigenvectors uˆi with optimal convergence
rates. Moreover, we prove that the non-outlier eigenvalues stick with those of
the unspiked matrices and the non-outlier eigenvectors are delocalized. The results
also hold near the so-called BBP transition and for degenerate spikes. On one
hand, our results can be regarded as a refinement of the counterparts of [12]
under additional regularity conditions. On the other hand, they can be viewed
as an analog of [34] by replacing the random matrix with i.i.d. entries with Haar
random matrix.
acknowledgement: The authors would like to thank the editor, the associated editor
and two anonymous referees for their many critical suggestions which have significantly
improved the paper. The authors are also grateful to Zhigang Bao and Ji Oon Lee
for many helpful discussions. The first author also wants to thank Hari Bercovici
for many useful comments. The first author is partially supported by National Science
Foundation DMS-2113489 and the second author is supported by ERC Advanced Grant
“RMTBeyond” No. 101020331.
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Xiucai
full_name: Ding, Xiucai
last_name: Ding
- first_name: Hong Chang
full_name: Ji, Hong Chang
id: dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d
last_name: Ji
citation:
ama: Ding X, Ji HC. Spiked multiplicative random matrices and principal components.
Stochastic Processes and their Applications. 2023;163:25-60. doi:10.1016/j.spa.2023.05.009
apa: Ding, X., & Ji, H. C. (2023). Spiked multiplicative random matrices and
principal components. Stochastic Processes and Their Applications. Elsevier.
https://doi.org/10.1016/j.spa.2023.05.009
chicago: Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices
and Principal Components.” Stochastic Processes and Their Applications.
Elsevier, 2023. https://doi.org/10.1016/j.spa.2023.05.009.
ieee: X. Ding and H. C. Ji, “Spiked multiplicative random matrices and principal
components,” Stochastic Processes and their Applications, vol. 163. Elsevier,
pp. 25–60, 2023.
ista: Ding X, Ji HC. 2023. Spiked multiplicative random matrices and principal components.
Stochastic Processes and their Applications. 163, 25–60.
mla: Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and
Principal Components.” Stochastic Processes and Their Applications, vol.
163, Elsevier, 2023, pp. 25–60, doi:10.1016/j.spa.2023.05.009.
short: X. Ding, H.C. Ji, Stochastic Processes and Their Applications 163 (2023)
25–60.
date_created: 2024-01-10T09:29:25Z
date_published: 2023-09-01T00:00:00Z
date_updated: 2024-01-16T08:49:51Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1016/j.spa.2023.05.009
ec_funded: 1
external_id:
arxiv:
- '2302.13502'
isi:
- '001113615900001'
file:
- access_level: open_access
checksum: 46a708b0cd5569a73d0f3d6c3e0a44dc
content_type: application/pdf
creator: dernst
date_created: 2024-01-16T08:47:31Z
date_updated: 2024-01-16T08:47:31Z
file_id: '14806'
file_name: 2023_StochasticProcAppl_Ding.pdf
file_size: 1870349
relation: main_file
success: 1
file_date_updated: 2024-01-16T08:47:31Z
has_accepted_license: '1'
intvolume: ' 163'
isi: 1
keyword:
- Applied Mathematics
- Modeling and Simulation
- Statistics and Probability
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 25-60
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Stochastic Processes and their Applications
publication_identifier:
eissn:
- 1879-209X
issn:
- 0304-4149
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: Spiked multiplicative random matrices and principal components
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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
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...