---
_id: '15025'
abstract:
- lang: eng
text: We consider quadratic forms of deterministic matrices A evaluated at the random
eigenvectors of a large N×N GOE or GUE matrix, or equivalently evaluated at the
columns of a Haar-orthogonal or Haar-unitary random matrix. We prove that, as
long as the deterministic matrix has rank much smaller than √N, the distributions
of the extrema of these quadratic forms are asymptotically the same as if the
eigenvectors were independent Gaussians. This reduces the problem to Gaussian
computations, which we carry out in several cases to illustrate our result, finding
Gumbel or Weibull limiting distributions depending on the signature of A. Our
result also naturally applies to the eigenvectors of any invariant ensemble.
acknowledgement: The first author was supported by the ERC Advanced Grant “RMTBeyond”
No. 101020331. The second author was supported by Fulbright Austria and the Austrian
Marshall Plan Foundation.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Benjamin
full_name: McKenna, Benjamin
id: b0cc634c-d549-11ee-96c8-87338c7ad808
last_name: McKenna
orcid: 0000-0003-2625-495X
citation:
ama: Erdös L, McKenna B. Extremal statistics of quadratic forms of GOE/GUE eigenvectors.
Annals of Applied Probability. 2024;34(1B):1623-1662. doi:10.1214/23-AAP2000
apa: Erdös, L., & McKenna, B. (2024). Extremal statistics of quadratic forms
of GOE/GUE eigenvectors. Annals of Applied Probability. Institute of Mathematical
Statistics. https://doi.org/10.1214/23-AAP2000
chicago: Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic
Forms of GOE/GUE Eigenvectors.” Annals of Applied Probability. Institute
of Mathematical Statistics, 2024. https://doi.org/10.1214/23-AAP2000.
ieee: L. Erdös and B. McKenna, “Extremal statistics of quadratic forms of GOE/GUE
eigenvectors,” Annals of Applied Probability, vol. 34, no. 1B. Institute
of Mathematical Statistics, pp. 1623–1662, 2024.
ista: Erdös L, McKenna B. 2024. Extremal statistics of quadratic forms of GOE/GUE
eigenvectors. Annals of Applied Probability. 34(1B), 1623–1662.
mla: Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms
of GOE/GUE Eigenvectors.” Annals of Applied Probability, vol. 34, no. 1B,
Institute of Mathematical Statistics, 2024, pp. 1623–62, doi:10.1214/23-AAP2000.
short: L. Erdös, B. McKenna, Annals of Applied Probability 34 (2024) 1623–1662.
date_created: 2024-02-25T23:00:56Z
date_published: 2024-02-01T00:00:00Z
date_updated: 2024-02-27T08:29:05Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/23-AAP2000
ec_funded: 1
external_id:
arxiv:
- '2208.12206'
intvolume: ' 34'
issue: 1B
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2208.12206
month: '02'
oa: 1
oa_version: Preprint
page: 1623-1662
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: 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: Extremal statistics of quadratic forms of GOE/GUE eigenvectors
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 34
year: '2024'
...
---
_id: '11741'
abstract:
- lang: eng
text: Following E. Wigner’s original vision, we prove that sampling the eigenvalue
gaps within the bulk spectrum of a fixed (deformed) Wigner matrix H yields the
celebrated Wigner-Dyson-Mehta universal statistics with high probability. Similarly,
we prove universality for a monoparametric family of deformed Wigner matrices
H+xA with a deterministic Hermitian matrix A and a fixed Wigner matrix H, just
using the randomness of a single scalar real random variable x. Both results constitute
quenched versions of bulk universality that has so far only been proven in annealed
sense with respect to the probability space of the matrix ensemble.
acknowledgement: "The authors are indebted to Sourav Chatterjee for forwarding the
very inspiring question that Stephen Shenker originally addressed to him which initiated
the current paper. They are also grateful that the authors of [23] kindly shared
their preliminary numerical results in June 2021.\r\nOpen access funding provided
by Institute of Science and Technology (IST Austria)."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
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. Quenched universality for deformed Wigner
matrices. Probability Theory and Related Fields. 2023;185:1183–1218. doi:10.1007/s00440-022-01156-7
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). Quenched universality
for deformed Wigner matrices. Probability Theory and Related Fields. Springer
Nature. https://doi.org/10.1007/s00440-022-01156-7
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Quenched Universality
for Deformed Wigner Matrices.” Probability Theory and Related Fields. Springer
Nature, 2023. https://doi.org/10.1007/s00440-022-01156-7.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Quenched universality for deformed
Wigner matrices,” Probability Theory and Related Fields, vol. 185. Springer
Nature, pp. 1183–1218, 2023.
ista: Cipolloni G, Erdös L, Schröder DJ. 2023. Quenched universality for deformed
Wigner matrices. Probability Theory and Related Fields. 185, 1183–1218.
mla: Cipolloni, Giorgio, et al. “Quenched Universality for Deformed Wigner Matrices.”
Probability Theory and Related Fields, vol. 185, Springer Nature, 2023,
pp. 1183–1218, doi:10.1007/s00440-022-01156-7.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields
185 (2023) 1183–1218.
date_created: 2022-08-07T22:02:00Z
date_published: 2023-04-01T00:00:00Z
date_updated: 2023-08-14T12:48:09Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00440-022-01156-7
external_id:
arxiv:
- '2106.10200'
isi:
- '000830344500001'
file:
- access_level: open_access
checksum: b9247827dae5544d1d19c37abe547abc
content_type: application/pdf
creator: dernst
date_created: 2023-08-14T12:47:32Z
date_updated: 2023-08-14T12:47:32Z
file_id: '14054'
file_name: 2023_ProbabilityTheory_Cipolloni.pdf
file_size: 782278
relation: main_file
success: 1
file_date_updated: 2023-08-14T12:47:32Z
has_accepted_license: '1'
intvolume: ' 185'
isi: 1
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 1183–1218
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- 1432-2064
issn:
- 0178-8051
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quenched universality for deformed 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 185
year: '2023'
...
---
_id: '14343'
abstract:
- lang: eng
text: The total energy of an eigenstate in a composite quantum system tends to be
distributed equally among its constituents. We identify the quantum fluctuation
around this equipartition principle in the simplest disordered quantum system
consisting of linear combinations of Wigner matrices. As our main ingredient,
we prove the Eigenstate Thermalisation Hypothesis and Gaussian fluctuation for
general quadratic forms of the bulk eigenvectors of Wigner matrices with an arbitrary
deformation.
acknowledgement: "G.C. and L.E. gratefully acknowledge many discussions with Dominik
Schröder at the preliminary stage of this project, especially his essential contribution
to identify the correct generalisation of traceless observables to the deformed
Wigner ensembles.\r\nL.E. and J.H. acknowledges support by ERC Advanced Grant ‘RMTBeyond’
No. 101020331."
article_number: e74
article_processing_charge: Yes
article_type: original
arxiv: 1
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: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- first_name: Oleksii
full_name: Kolupaiev, Oleksii
id: 149b70d4-896a-11ed-bdf8-8c63fd44ca61
last_name: Kolupaiev
citation:
ama: Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Gaussian fluctuations in the
equipartition principle for Wigner matrices. Forum of Mathematics, Sigma.
2023;11. doi:10.1017/fms.2023.70
apa: Cipolloni, G., Erdös, L., Henheik, S. J., & Kolupaiev, O. (2023). Gaussian
fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics,
Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2023.70
chicago: Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev.
“Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” Forum
of Mathematics, Sigma. Cambridge University Press, 2023. https://doi.org/10.1017/fms.2023.70.
ieee: G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Gaussian fluctuations
in the equipartition principle for Wigner matrices,” Forum of Mathematics,
Sigma, vol. 11. Cambridge University Press, 2023.
ista: Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2023. Gaussian fluctuations
in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma.
11, e74.
mla: Cipolloni, Giorgio, et al. “Gaussian Fluctuations in the Equipartition Principle
for Wigner Matrices.” Forum of Mathematics, Sigma, vol. 11, e74, Cambridge
University Press, 2023, doi:10.1017/fms.2023.70.
short: G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Forum of Mathematics,
Sigma 11 (2023).
date_created: 2023-09-17T22:01:09Z
date_published: 2023-08-23T00:00:00Z
date_updated: 2023-12-13T12:24:23Z
day: '23'
ddc:
- '510'
department:
- _id: LaEr
- _id: GradSch
doi: 10.1017/fms.2023.70
ec_funded: 1
external_id:
arxiv:
- '2301.05181'
isi:
- '001051980200001'
file:
- access_level: open_access
checksum: eb747420e6a88a7796fa934151957676
content_type: application/pdf
creator: dernst
date_created: 2023-09-20T11:09:35Z
date_updated: 2023-09-20T11:09:35Z
file_id: '14352'
file_name: 2023_ForumMathematics_Cipolloni.pdf
file_size: 852652
relation: main_file
success: 1
file_date_updated: 2023-09-20T11:09:35Z
has_accepted_license: '1'
intvolume: ' 11'
isi: 1
language:
- iso: eng
month: '08'
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: Forum of Mathematics, Sigma
publication_identifier:
eissn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Gaussian fluctuations in the equipartition principle 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 11
year: '2023'
...
---
_id: '14408'
abstract:
- lang: eng
text: "We prove that the mesoscopic linear statistics ∑if(na(σi−z0)) of the eigenvalues
{σi}i of large n×n non-Hermitian random matrices with complex centred i.i.d. entries
are asymptotically Gaussian for any H20-functions f around any point z0 in the
bulk of the spectrum on any mesoscopic scale 0Probability Theory and Related Fields. 2023. doi:10.1007/s00440-023-01229-1
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). Mesoscopic central
limit theorem for non-Hermitian random matrices. Probability Theory and Related
Fields. Springer Nature. https://doi.org/10.1007/s00440-023-01229-1
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Mesoscopic Central
Limit Theorem for Non-Hermitian Random Matrices.” Probability Theory and Related
Fields. Springer Nature, 2023. https://doi.org/10.1007/s00440-023-01229-1.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Mesoscopic central limit theorem
for non-Hermitian random matrices,” Probability Theory and Related Fields.
Springer Nature, 2023.
ista: Cipolloni G, Erdös L, Schröder DJ. 2023. Mesoscopic central limit theorem
for non-Hermitian random matrices. Probability Theory and Related Fields.
mla: Cipolloni, Giorgio, et al. “Mesoscopic Central Limit Theorem for Non-Hermitian
Random Matrices.” Probability Theory and Related Fields, Springer Nature,
2023, doi:10.1007/s00440-023-01229-1.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields
(2023).
date_created: 2023-10-08T22:01:17Z
date_published: 2023-09-28T00:00:00Z
date_updated: 2023-10-09T07:19:01Z
day: '28'
department:
- _id: LaEr
doi: 10.1007/s00440-023-01229-1
external_id:
arxiv:
- '2210.12060'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2210.12060
month: '09'
oa: 1
oa_version: Preprint
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- 1432-2064
issn:
- 0178-8051
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Mesoscopic central limit theorem for non-Hermitian random matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_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
arxiv: 1
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: '14849'
abstract:
- lang: eng
text: We establish a precise three-term asymptotic expansion, with an optimal estimate
of the error term, for the rightmost eigenvalue of an n×n random matrix with independent
identically distributed complex entries as n tends to infinity. All terms in the
expansion are universal.
acknowledgement: "The second and the fourth author were supported by the ERC Advanced
Grant\r\n“RMTBeyond” No. 101020331. The third author was supported by Dr. Max Rössler,
the\r\nWalter Haefner Foundation and the ETH Zürich Foundation."
article_processing_charge: No
article_type: original
arxiv: 1
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
last_name: Xu
citation:
ama: Cipolloni G, Erdös L, Schröder DJ, Xu Y. On the rightmost eigenvalue of non-Hermitian
random matrices. The Annals of Probability. 2023;51(6):2192-2242. doi:10.1214/23-aop1643
apa: Cipolloni, G., Erdös, L., Schröder, D. J., & Xu, Y. (2023). On the rightmost
eigenvalue of non-Hermitian random matrices. The Annals of Probability.
Institute of Mathematical Statistics. https://doi.org/10.1214/23-aop1643
chicago: Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu.
“On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” The Annals
of Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/23-aop1643.
ieee: G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “On the rightmost eigenvalue
of non-Hermitian random matrices,” The Annals of Probability, vol. 51,
no. 6. Institute of Mathematical Statistics, pp. 2192–2242, 2023.
ista: Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2023. On the rightmost eigenvalue
of non-Hermitian random matrices. The Annals of Probability. 51(6), 2192–2242.
mla: Cipolloni, Giorgio, et al. “On the Rightmost Eigenvalue of Non-Hermitian Random
Matrices.” The Annals of Probability, vol. 51, no. 6, Institute of Mathematical
Statistics, 2023, pp. 2192–242, doi:10.1214/23-aop1643.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, The Annals of Probability 51
(2023) 2192–2242.
date_created: 2024-01-22T08:08:41Z
date_published: 2023-11-01T00:00:00Z
date_updated: 2024-01-23T10:56:30Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/23-aop1643
ec_funded: 1
external_id:
arxiv:
- '2206.04448'
intvolume: ' 51'
issue: '6'
keyword:
- Statistics
- Probability and Uncertainty
- Statistics and Probability
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2206.04448
month: '11'
oa: 1
oa_version: Preprint
page: 2192-2242
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: The Annals of Probability
publication_identifier:
issn:
- 0091-1798
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
status: public
title: On the rightmost eigenvalue of non-Hermitian random matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 51
year: '2023'
...
---
_id: '13317'
abstract:
- lang: eng
text: We prove the Eigenstate Thermalisation Hypothesis (ETH) for local observables
in a typical translation invariant system of quantum spins with L-body interactions,
where L is the number of spins. This mathematically verifies the observation first
made by Santos and Rigol (Phys Rev E 82(3):031130, 2010, https://doi.org/10.1103/PhysRevE.82.031130)
that the ETH may hold for systems with additional translational symmetries for
a naturally restricted class of observables. We also present numerical support
for the same phenomenon for Hamiltonians with local interaction.
acknowledgement: "LE, JH, and VR were supported by ERC Advanced Grant “RMTBeyond”
No. 101020331. SS was supported by KAKENHI Grant Number JP22J14935 from the Japan
Society for the Promotion of Science (JSPS) and Forefront Physics and Mathematics
Program to Drive Transformation (FoPM), a World-leading Innovative Graduate Study
(WINGS) Program, the University of Tokyo.\r\nOpen access funding provided by The
University of Tokyo."
article_number: '128'
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Shoki
full_name: Sugimoto, Shoki
last_name: Sugimoto
- 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: Volodymyr
full_name: Riabov, Volodymyr
id: 1949f904-edfb-11eb-afb5-e2dfddabb93b
last_name: Riabov
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
citation:
ama: Sugimoto S, Henheik SJ, Riabov V, Erdös L. Eigenstate thermalisation hypothesis
for translation invariant spin systems. Journal of Statistical Physics.
2023;190(7). doi:10.1007/s10955-023-03132-4
apa: Sugimoto, S., Henheik, S. J., Riabov, V., & Erdös, L. (2023). Eigenstate
thermalisation hypothesis for translation invariant spin systems. Journal of
Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-023-03132-4
chicago: Sugimoto, Shoki, Sven Joscha Henheik, Volodymyr Riabov, and László Erdös.
“Eigenstate Thermalisation Hypothesis for Translation Invariant Spin Systems.”
Journal of Statistical Physics. Springer Nature, 2023. https://doi.org/10.1007/s10955-023-03132-4.
ieee: S. Sugimoto, S. J. Henheik, V. Riabov, and L. Erdös, “Eigenstate thermalisation
hypothesis for translation invariant spin systems,” Journal of Statistical
Physics, vol. 190, no. 7. Springer Nature, 2023.
ista: Sugimoto S, Henheik SJ, Riabov V, Erdös L. 2023. Eigenstate thermalisation
hypothesis for translation invariant spin systems. Journal of Statistical Physics.
190(7), 128.
mla: Sugimoto, Shoki, et al. “Eigenstate Thermalisation Hypothesis for Translation
Invariant Spin Systems.” Journal of Statistical Physics, vol. 190, no.
7, 128, Springer Nature, 2023, doi:10.1007/s10955-023-03132-4.
short: S. Sugimoto, S.J. Henheik, V. Riabov, L. Erdös, Journal of Statistical Physics
190 (2023).
date_created: 2023-07-30T22:01:02Z
date_published: 2023-07-21T00:00:00Z
date_updated: 2023-12-13T11:38:44Z
day: '21'
ddc:
- '510'
- '530'
department:
- _id: LaEr
doi: 10.1007/s10955-023-03132-4
ec_funded: 1
external_id:
arxiv:
- '2304.04213'
isi:
- '001035677200002'
file:
- access_level: open_access
checksum: c2ef6b2aecfee1ad6d03fab620507c2c
content_type: application/pdf
creator: dernst
date_created: 2023-07-31T07:49:31Z
date_updated: 2023-07-31T07:49:31Z
file_id: '13325'
file_name: 2023_JourStatPhysics_Sugimoto.pdf
file_size: 612755
relation: main_file
success: 1
file_date_updated: 2023-07-31T07:49:31Z
has_accepted_license: '1'
intvolume: ' 190'
isi: 1
issue: '7'
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: Eigenstate thermalisation hypothesis for translation invariant spin 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 190
year: '2023'
...
---
_id: '10405'
abstract:
- lang: eng
text: 'We consider large non-Hermitian random matrices X with complex, independent,
identically distributed centred entries and show that the linear statistics of
their eigenvalues are asymptotically Gaussian for test functions having 2+ϵ derivatives.
Previously this result was known only for a few special cases; either the test
functions were required to be analytic [72], or the distribution of the matrix
elements needed to be Gaussian [73], or at least match the Gaussian up to the
first four moments [82, 56]. We find the exact dependence of the limiting variance
on the fourth cumulant that was not known before. The proof relies on two novel
ingredients: (i) a local law for a product of two resolvents of the Hermitisation
of X with different spectral parameters and (ii) a coupling of several weakly
dependent Dyson Brownian motions. These methods are also the key inputs for our
analogous results on the linear eigenvalue statistics of real matrices X that
are presented in the companion paper [32]. '
acknowledgement: L.E. would like to thank Nathanaël Berestycki and D.S.would like
to thank Nina Holden for valuable discussions on the Gaussian freefield.G.C. and
L.E. are partially supported by ERC Advanced Grant No. 338804.G.C. received funding
from the European Union’s Horizon 2020 research and in-novation programme under
the Marie Skłodowska-Curie Grant Agreement No.665385. D.S. is supported by Dr. Max
Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
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. Central limit theorem for linear eigenvalue
statistics of non-Hermitian random matrices. Communications on Pure and Applied
Mathematics. 2023;76(5):946-1034. doi:10.1002/cpa.22028
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). Central limit theorem
for linear eigenvalue statistics of non-Hermitian random matrices. Communications
on Pure and Applied Mathematics. Wiley. https://doi.org/10.1002/cpa.22028
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Central Limit
Theorem for Linear Eigenvalue Statistics of Non-Hermitian Random Matrices.” Communications
on Pure and Applied Mathematics. Wiley, 2023. https://doi.org/10.1002/cpa.22028.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Central limit theorem for linear
eigenvalue statistics of non-Hermitian random matrices,” Communications on
Pure and Applied Mathematics, vol. 76, no. 5. Wiley, pp. 946–1034, 2023.
ista: Cipolloni G, Erdös L, Schröder DJ. 2023. Central limit theorem for linear
eigenvalue statistics of non-Hermitian random matrices. Communications on Pure
and Applied Mathematics. 76(5), 946–1034.
mla: Cipolloni, Giorgio, et al. “Central Limit Theorem for Linear Eigenvalue Statistics
of Non-Hermitian Random Matrices.” Communications on Pure and Applied Mathematics,
vol. 76, no. 5, Wiley, 2023, pp. 946–1034, doi:10.1002/cpa.22028.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Communications on Pure and Applied
Mathematics 76 (2023) 946–1034.
date_created: 2021-12-05T23:01:41Z
date_published: 2023-05-01T00:00:00Z
date_updated: 2023-10-04T09:22:55Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1002/cpa.22028
ec_funded: 1
external_id:
arxiv:
- '1912.04100'
isi:
- '000724652500001'
file:
- access_level: open_access
checksum: 8346bc2642afb4ccb7f38979f41df5d9
content_type: application/pdf
creator: dernst
date_created: 2023-10-04T09:21:48Z
date_updated: 2023-10-04T09:21:48Z
file_id: '14388'
file_name: 2023_CommPureMathematics_Cipolloni.pdf
file_size: 803440
relation: main_file
success: 1
file_date_updated: 2023-10-04T09:21:48Z
has_accepted_license: '1'
intvolume: ' 76'
isi: 1
issue: '5'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 946-1034
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: Communications on Pure and Applied Mathematics
publication_identifier:
eissn:
- 1097-0312
issn:
- 0010-3640
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: Central limit theorem for linear eigenvalue statistics of non-Hermitian random
matrices
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 76
year: '2023'
...
---
_id: '12683'
abstract:
- lang: eng
text: We study the eigenvalue trajectories of a time dependent matrix Gt=H+itvv∗
for t≥0, where H is an N×N Hermitian random matrix and v is a unit vector. In
particular, we establish that with high probability, an outlier can be distinguished
at all times t>1+N−1/3+ϵ, for any ϵ>0. The study of this natural process combines
elements of Hermitian and non-Hermitian analysis, and illustrates some aspects
of the intrinsic instability of (even weakly) non-Hermitian matrices.
acknowledgement: G. Dubach gratefully acknowledges funding from the European Union’s
Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
Grant Agreement No. 754411. L. Erdős is supported by ERC Advanced Grant “RMTBeyond”
No. 101020331.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Guillaume
full_name: Dubach, Guillaume
id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E
last_name: Dubach
orcid: 0000-0001-6892-8137
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
citation:
ama: Dubach G, Erdös L. Dynamics of a rank-one perturbation of a Hermitian matrix.
Electronic Communications in Probability. 2023;28:1-13. doi:10.1214/23-ECP516
apa: Dubach, G., & Erdös, L. (2023). Dynamics of a rank-one perturbation of
a Hermitian matrix. Electronic Communications in Probability. Institute
of Mathematical Statistics. https://doi.org/10.1214/23-ECP516
chicago: Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation
of a Hermitian Matrix.” Electronic Communications in Probability. Institute
of Mathematical Statistics, 2023. https://doi.org/10.1214/23-ECP516.
ieee: G. Dubach and L. Erdös, “Dynamics of a rank-one perturbation of a Hermitian
matrix,” Electronic Communications in Probability, vol. 28. Institute of
Mathematical Statistics, pp. 1–13, 2023.
ista: Dubach G, Erdös L. 2023. Dynamics of a rank-one perturbation of a Hermitian
matrix. Electronic Communications in Probability. 28, 1–13.
mla: Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of
a Hermitian Matrix.” Electronic Communications in Probability, vol. 28,
Institute of Mathematical Statistics, 2023, pp. 1–13, doi:10.1214/23-ECP516.
short: G. Dubach, L. Erdös, Electronic Communications in Probability 28 (2023) 1–13.
date_created: 2023-02-26T23:01:01Z
date_published: 2023-02-08T00:00:00Z
date_updated: 2023-10-17T12:48:10Z
day: '08'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1214/23-ECP516
ec_funded: 1
external_id:
arxiv:
- '2108.13694'
isi:
- '000950650200005'
file:
- access_level: open_access
checksum: a1c6f0a3e33688fd71309c86a9aad86e
content_type: application/pdf
creator: dernst
date_created: 2023-02-27T09:43:27Z
date_updated: 2023-02-27T09:43:27Z
file_id: '12692'
file_name: 2023_ElectCommProbability_Dubach.pdf
file_size: 479105
relation: main_file
success: 1
file_date_updated: 2023-02-27T09:43:27Z
has_accepted_license: '1'
intvolume: ' 28'
isi: 1
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 1-13
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Electronic Communications in Probability
publication_identifier:
eissn:
- 1083-589X
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Dynamics of a rank-one perturbation of a Hermitian matrix
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: 28
year: '2023'
...
---
_id: '12707'
abstract:
- lang: eng
text: We establish precise right-tail small deviation estimates for the largest
eigenvalue of real symmetric and complex Hermitian matrices whose entries are
independent random variables with uniformly bounded moments. The proof relies
on a Green function comparison along a continuous interpolating matrix flow for
a long time. Less precise estimates are also obtained in the left tail.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Yuanyuan
full_name: Xu, Yuanyuan
id: 7902bdb1-a2a4-11eb-a164-c9216f71aea3
last_name: Xu
orcid: 0000-0003-1559-1205
citation:
ama: Erdös L, Xu Y. Small deviation estimates for the largest eigenvalue of Wigner
matrices. Bernoulli. 2023;29(2):1063-1079. doi:10.3150/22-BEJ1490
apa: Erdös, L., & Xu, Y. (2023). Small deviation estimates for the largest eigenvalue
of Wigner matrices. Bernoulli. Bernoulli Society for Mathematical Statistics
and Probability. https://doi.org/10.3150/22-BEJ1490
chicago: Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest
Eigenvalue of Wigner Matrices.” Bernoulli. Bernoulli Society for Mathematical
Statistics and Probability, 2023. https://doi.org/10.3150/22-BEJ1490.
ieee: L. Erdös and Y. Xu, “Small deviation estimates for the largest eigenvalue
of Wigner matrices,” Bernoulli, vol. 29, no. 2. Bernoulli Society for Mathematical
Statistics and Probability, pp. 1063–1079, 2023.
ista: Erdös L, Xu Y. 2023. Small deviation estimates for the largest eigenvalue
of Wigner matrices. Bernoulli. 29(2), 1063–1079.
mla: Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest
Eigenvalue of Wigner Matrices.” Bernoulli, vol. 29, no. 2, Bernoulli Society
for Mathematical Statistics and Probability, 2023, pp. 1063–79, doi:10.3150/22-BEJ1490.
short: L. Erdös, Y. Xu, Bernoulli 29 (2023) 1063–1079.
date_created: 2023-03-05T23:01:05Z
date_published: 2023-05-01T00:00:00Z
date_updated: 2023-10-04T10:21:07Z
day: '01'
department:
- _id: LaEr
doi: 10.3150/22-BEJ1490
ec_funded: 1
external_id:
arxiv:
- '2112.12093 '
isi:
- '000947270100008'
intvolume: ' 29'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2112.12093
month: '05'
oa: 1
oa_version: Preprint
page: 1063-1079
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Bernoulli
publication_identifier:
issn:
- 1350-7265
publication_status: published
publisher: Bernoulli Society for Mathematical Statistics and Probability
quality_controlled: '1'
scopus_import: '1'
status: public
title: Small deviation estimates for the largest eigenvalue of Wigner matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 29
year: '2023'
...
---
_id: '12761'
abstract:
- lang: eng
text: "We consider the fluctuations of regular functions f of a Wigner matrix W
viewed as an entire matrix f (W). Going beyond the well-studied tracial mode,
Trf (W), which is equivalent to the customary linear statistics of eigenvalues,
we show that Trf (W)A is asymptotically normal for any nontrivial bounded deterministic
matrix A. We identify three different and asymptotically independent modes of
this fluctuation, corresponding to the tracial part, the traceless diagonal part
and the off-diagonal part of f (W) in the entire mesoscopic regime, where we find
that the off-diagonal modes fluctuate on a much smaller scale than the tracial
mode. As a main motivation to study CLT in such generality on small mesoscopic
scales, we determine\r\nthe fluctuations in the eigenstate thermalization hypothesis
(Phys. Rev. A 43 (1991) 2046–2049), that is, prove that the eigenfunction overlaps
with any deterministic matrix are asymptotically Gaussian after a small spectral
averaging. Finally, in the macroscopic regime our result also generalizes (Zh.
Mat. Fiz. Anal. Geom. 9 (2013) 536–581, 611, 615) to complex W and to all crossover
ensembles in between. The main technical inputs are the recent\r\nmultiresolvent
local laws with traceless deterministic matrices from the companion paper (Comm.
Math. Phys. 388 (2021) 1005–1048)."
acknowledgement: The second author is partially funded by the ERC Advanced Grant “RMTBEYOND”
No. 101020331. The third author is supported by Dr. Max Rössler, the Walter Haefner
Foundation and the ETH Zürich Foundation.
article_processing_charge: No
article_type: original
arxiv: 1
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. Functional central limit theorems for Wigner
matrices. Annals of Applied Probability. 2023;33(1):447-489. doi:10.1214/22-AAP1820
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). Functional central
limit theorems for Wigner matrices. Annals of Applied Probability. Institute
of Mathematical Statistics. https://doi.org/10.1214/22-AAP1820
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Functional Central
Limit Theorems for Wigner Matrices.” Annals of Applied Probability. Institute
of Mathematical Statistics, 2023. https://doi.org/10.1214/22-AAP1820.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Functional central limit theorems
for Wigner matrices,” Annals of Applied Probability, vol. 33, no. 1. Institute
of Mathematical Statistics, pp. 447–489, 2023.
ista: Cipolloni G, Erdös L, Schröder DJ. 2023. Functional central limit theorems
for Wigner matrices. Annals of Applied Probability. 33(1), 447–489.
mla: Cipolloni, Giorgio, et al. “Functional Central Limit Theorems for Wigner Matrices.”
Annals of Applied Probability, vol. 33, no. 1, Institute of Mathematical
Statistics, 2023, pp. 447–89, doi:10.1214/22-AAP1820.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Applied Probability 33 (2023)
447–489.
date_created: 2023-03-26T22:01:08Z
date_published: 2023-02-01T00:00:00Z
date_updated: 2023-10-17T12:48:52Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/22-AAP1820
ec_funded: 1
external_id:
arxiv:
- '2012.13218'
isi:
- '000946432400015'
intvolume: ' 33'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2012.13218
month: '02'
oa: 1
oa_version: Preprint
page: 447-489
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: 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: Functional central limit theorems for Wigner matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 33
year: '2023'
...
---
_id: '12792'
abstract:
- lang: eng
text: In the physics literature the spectral form factor (SFF), the squared Fourier
transform of the empirical eigenvalue density, is the most common tool to test
universality for disordered quantum systems, yet previous mathematical results
have been restricted only to two exactly solvable models (Forrester in J Stat
Phys 183:33, 2021. https://doi.org/10.1007/s10955-021-02767-5, Commun Math Phys
387:215–235, 2021. https://doi.org/10.1007/s00220-021-04193-w). We rigorously
prove the physics prediction on SFF up to an intermediate time scale for a large
class of random matrices using a robust method, the multi-resolvent local laws.
Beyond Wigner matrices we also consider the monoparametric ensemble and prove
that universality of SFF can already be triggered by a single random parameter,
supplementing the recently proven Wigner–Dyson universality (Cipolloni et al.
in Probab Theory Relat Fields, 2021. https://doi.org/10.1007/s00440-022-01156-7)
to larger spectral scales. Remarkably, extensive numerics indicates that our formulas
correctly predict the SFF in the entire slope-dip-ramp regime, as customarily
called in physics.
acknowledgement: "We are grateful to the authors of [25] for sharing with us their
insights and preliminary numerical results. We are especially thankful to Stephen
Shenker for very valuable advice over several email communications. Helpful comments
on the manuscript from Peter Forrester and from the anonymous referees are also
acknowledged.\r\nOpen access funding provided by Institute of Science and Technology
(IST Austria).\r\nLászló Erdős: Partially supported by ERC Advanced Grant \"RMTBeyond\"
No. 101020331. Dominik Schröder: Supported by Dr. Max Rössler, the Walter Haefner
Foundation and the ETH Zürich Foundation."
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
citation:
ama: Cipolloni G, Erdös L, Schröder DJ. On the spectral form factor for random matrices.
Communications in Mathematical Physics. 2023;401:1665-1700. doi:10.1007/s00220-023-04692-y
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). On the spectral form
factor for random matrices. Communications in Mathematical Physics. Springer
Nature. https://doi.org/10.1007/s00220-023-04692-y
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Spectral
Form Factor for Random Matrices.” Communications in Mathematical Physics.
Springer Nature, 2023. https://doi.org/10.1007/s00220-023-04692-y.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “On the spectral form factor for
random matrices,” Communications in Mathematical Physics, vol. 401. Springer
Nature, pp. 1665–1700, 2023.
ista: Cipolloni G, Erdös L, Schröder DJ. 2023. On the spectral form factor for random
matrices. Communications in Mathematical Physics. 401, 1665–1700.
mla: Cipolloni, Giorgio, et al. “On the Spectral Form Factor for Random Matrices.”
Communications in Mathematical Physics, vol. 401, Springer Nature, 2023,
pp. 1665–700, doi:10.1007/s00220-023-04692-y.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics
401 (2023) 1665–1700.
date_created: 2023-04-02T22:01:11Z
date_published: 2023-07-01T00:00:00Z
date_updated: 2023-10-04T12:10:31Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00220-023-04692-y
ec_funded: 1
external_id:
isi:
- '000957343500001'
file:
- access_level: open_access
checksum: 72057940f76654050ca84a221f21786c
content_type: application/pdf
creator: dernst
date_created: 2023-10-04T12:09:18Z
date_updated: 2023-10-04T12:09:18Z
file_id: '14397'
file_name: 2023_CommMathPhysics_Cipolloni.pdf
file_size: 859967
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intvolume: ' 401'
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language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 1665-1700
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the spectral form factor for 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: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 401
year: '2023'
...
---
_id: '10732'
abstract:
- lang: eng
text: We compute the deterministic approximation of products of Sobolev functions
of large Wigner matrices W and provide an optimal error bound on their fluctuation
with very high probability. This generalizes Voiculescu's seminal theorem from
polynomials to general Sobolev functions, as well as from tracial quantities to
individual matrix elements. Applying the result to eitW for large t, we obtain
a precise decay rate for the overlaps of several deterministic matrices with temporally
well separated Heisenberg time evolutions; thus we demonstrate the thermalisation
effect of the unitary group generated by Wigner matrices.
acknowledgement: We compute the deterministic approximation of products of Sobolev
functions of large Wigner matrices W and provide an optimal error bound on their
fluctuation with very high probability. This generalizes Voiculescu's seminal theorem
from polynomials to general Sobolev functions, as well as from tracial quantities
to individual matrix elements. Applying the result to for large t, we obtain a
precise decay rate for the overlaps of several deterministic matrices with temporally
well separated Heisenberg time evolutions; thus we demonstrate the thermalisation
effect of the unitary group generated by Wigner matrices.
article_number: '109394'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
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. Thermalisation for Wigner matrices. Journal
of Functional Analysis. 2022;282(8). doi:10.1016/j.jfa.2022.109394
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Thermalisation for
Wigner matrices. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2022.109394
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Thermalisation
for Wigner Matrices.” Journal of Functional Analysis. Elsevier, 2022. https://doi.org/10.1016/j.jfa.2022.109394.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Thermalisation for Wigner matrices,”
Journal of Functional Analysis, vol. 282, no. 8. Elsevier, 2022.
ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Thermalisation for Wigner matrices.
Journal of Functional Analysis. 282(8), 109394.
mla: Cipolloni, Giorgio, et al. “Thermalisation for Wigner Matrices.” Journal
of Functional Analysis, vol. 282, no. 8, 109394, Elsevier, 2022, doi:10.1016/j.jfa.2022.109394.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Journal of Functional Analysis 282
(2022).
date_created: 2022-02-06T23:01:30Z
date_published: 2022-04-15T00:00:00Z
date_updated: 2023-08-02T14:12:35Z
day: '15'
ddc:
- '500'
department:
- _id: LaEr
doi: 10.1016/j.jfa.2022.109394
external_id:
arxiv:
- '2102.09975'
isi:
- '000781239100004'
file:
- access_level: open_access
checksum: b75fdad606ab507dc61109e0907d86c0
content_type: application/pdf
creator: dernst
date_created: 2022-07-29T07:22:08Z
date_updated: 2022-07-29T07:22:08Z
file_id: '11690'
file_name: 2022_JourFunctionalAnalysis_Cipolloni.pdf
file_size: 652573
relation: main_file
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file_date_updated: 2022-07-29T07:22:08Z
has_accepted_license: '1'
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issue: '8'
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- iso: eng
month: '04'
oa: 1
oa_version: Published Version
publication: Journal of Functional Analysis
publication_identifier:
eissn:
- 1096-0783
issn:
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publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Thermalisation 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: 282
year: '2022'
...
---
_id: '11418'
abstract:
- lang: eng
text: "We consider the quadratic form of a general high-rank deterministic matrix
on the eigenvectors of an N×N\r\nWigner matrix and prove that it has Gaussian
fluctuation for each bulk eigenvector in the large N limit. The proof is a combination
of the energy method for the Dyson Brownian motion inspired by Marcinek and Yau
(2021) and our recent multiresolvent local laws (Comm. Math. Phys. 388 (2021)
1005–1048)."
acknowledgement: L.E. would like to thank Zhigang Bao for many illuminating discussions
in an early stage of this research. The authors are also grateful to Paul Bourgade
for his comments on the manuscript and the anonymous referee for several useful
suggestions.
article_processing_charge: No
article_type: original
arxiv: 1
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. Normal fluctuation in quantum ergodicity
for Wigner matrices. Annals of Probability. 2022;50(3):984-1012. doi:10.1214/21-AOP1552
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Normal fluctuation
in quantum ergodicity for Wigner matrices. Annals of Probability. Institute
of Mathematical Statistics. https://doi.org/10.1214/21-AOP1552
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Normal Fluctuation
in Quantum Ergodicity for Wigner Matrices.” Annals of Probability. Institute
of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AOP1552.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Normal fluctuation in quantum
ergodicity for Wigner matrices,” Annals of Probability, vol. 50, no. 3.
Institute of Mathematical Statistics, pp. 984–1012, 2022.
ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Normal fluctuation in quantum ergodicity
for Wigner matrices. Annals of Probability. 50(3), 984–1012.
mla: Cipolloni, Giorgio, et al. “Normal Fluctuation in Quantum Ergodicity for Wigner
Matrices.” Annals of Probability, vol. 50, no. 3, Institute of Mathematical
Statistics, 2022, pp. 984–1012, doi:10.1214/21-AOP1552.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Probability 50 (2022) 984–1012.
date_created: 2022-05-29T22:01:53Z
date_published: 2022-05-01T00:00:00Z
date_updated: 2023-08-03T07:16:53Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/21-AOP1552
external_id:
arxiv:
- '2103.06730'
isi:
- '000793963400005'
intvolume: ' 50'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2103.06730
month: '05'
oa: 1
oa_version: Preprint
page: 984-1012
publication: Annals of Probability
publication_identifier:
eissn:
- 2168-894X
issn:
- 0091-1798
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Normal fluctuation in quantum ergodicity for Wigner matrices
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 50
year: '2022'
...
---
_id: '12148'
abstract:
- lang: eng
text: 'We prove a general local law for Wigner matrices that optimally handles observables
of arbitrary rank and thus unifies the well-known averaged and isotropic local
laws. As an application, we prove a central limit theorem in quantum unique ergodicity
(QUE): that is, we show that the quadratic forms of a general deterministic matrix
A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation.
For the bulk spectrum, we thus generalise our previous result [17] as valid for
test matrices A of large rank as well as the result of Benigni and Lopatto [7]
as valid for specific small-rank observables.'
acknowledgement: L.E. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331.
D.S. acknowledges the support of Dr. Max Rössler, the Walter Haefner Foundation
and the ETH Zürich Foundation.
article_number: e96
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. Rank-uniform local law for Wigner matrices.
Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2022.86
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Rank-uniform local
law for Wigner matrices. Forum of Mathematics, Sigma. Cambridge University
Press. https://doi.org/10.1017/fms.2022.86
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Rank-Uniform
Local Law for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge
University Press, 2022. https://doi.org/10.1017/fms.2022.86.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner
matrices,” Forum of Mathematics, Sigma, vol. 10. Cambridge University Press,
2022.
ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner
matrices. Forum of Mathematics, Sigma. 10, e96.
mla: Cipolloni, Giorgio, et al. “Rank-Uniform Local Law for Wigner Matrices.” Forum
of Mathematics, Sigma, vol. 10, e96, Cambridge University Press, 2022, doi:10.1017/fms.2022.86.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022).
date_created: 2023-01-12T12:07:30Z
date_published: 2022-10-27T00:00:00Z
date_updated: 2023-08-04T09:00:35Z
day: '27'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1017/fms.2022.86
ec_funded: 1
external_id:
isi:
- '000873719200001'
file:
- access_level: open_access
checksum: 94a049aeb1eea5497aa097712a73c400
content_type: application/pdf
creator: dernst
date_created: 2023-01-24T10:02:40Z
date_updated: 2023-01-24T10:02:40Z
file_id: '12356'
file_name: 2022_ForumMath_Cipolloni.pdf
file_size: 817089
relation: main_file
success: 1
file_date_updated: 2023-01-24T10:02:40Z
has_accepted_license: '1'
intvolume: ' 10'
isi: 1
keyword:
- Computational Mathematics
- Discrete Mathematics and Combinatorics
- Geometry and Topology
- Mathematical Physics
- Statistics and Probability
- Algebra and Number Theory
- Theoretical Computer Science
- Analysis
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: Forum of Mathematics, Sigma
publication_identifier:
issn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Rank-uniform local law 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: 10
year: '2022'
...
---
_id: '12179'
abstract:
- lang: eng
text: We derive an accurate lower tail estimate on the lowest singular value σ1(X−z)
of a real Gaussian (Ginibre) random matrix X shifted by a complex parameter z.
Such shift effectively changes the upper tail behavior of the condition number
κ(X−z) from the slower (κ(X−z)≥t)≲1/t decay typical for real Ginibre matrices
to the faster 1/t2 decay seen for complex Ginibre matrices as long as z is away
from the real axis. This sharpens and resolves a recent conjecture in [J. Banks
et al., https://arxiv.org/abs/2005.08930, 2020] on the regularizing effect of
the real Ginibre ensemble with a genuinely complex shift. As a consequence we
obtain an improved upper bound on the eigenvalue condition numbers (known also
as the eigenvector overlaps) for real Ginibre matrices. The main technical tool
is a rigorous supersymmetric analysis from our earlier work [Probab. Math. Phys.,
1 (2020), pp. 101--146].
article_processing_charge: No
article_type: original
arxiv: 1
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. On the condition number of the shifted real
Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. 2022;43(3):1469-1487.
doi:10.1137/21m1424408
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). On the condition number
of the shifted real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications.
Society for Industrial and Applied Mathematics. https://doi.org/10.1137/21m1424408
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Condition
Number of the Shifted Real Ginibre Ensemble.” SIAM Journal on Matrix Analysis
and Applications. Society for Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/21m1424408.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “On the condition number of the
shifted real Ginibre ensemble,” SIAM Journal on Matrix Analysis and Applications,
vol. 43, no. 3. Society for Industrial and Applied Mathematics, pp. 1469–1487,
2022.
ista: Cipolloni G, Erdös L, Schröder DJ. 2022. On the condition number of the shifted
real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. 43(3),
1469–1487.
mla: Cipolloni, Giorgio, et al. “On the Condition Number of the Shifted Real Ginibre
Ensemble.” SIAM Journal on Matrix Analysis and Applications, vol. 43, no.
3, Society for Industrial and Applied Mathematics, 2022, pp. 1469–87, doi:10.1137/21m1424408.
short: G. Cipolloni, L. Erdös, D.J. Schröder, SIAM Journal on Matrix Analysis and
Applications 43 (2022) 1469–1487.
date_created: 2023-01-12T12:12:38Z
date_published: 2022-07-01T00:00:00Z
date_updated: 2023-01-27T06:56:06Z
day: '01'
department:
- _id: LaEr
doi: 10.1137/21m1424408
external_id:
arxiv:
- '2105.13719'
intvolume: ' 43'
issue: '3'
keyword:
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2105.13719
month: '07'
oa: 1
oa_version: Preprint
page: 1469-1487
publication: SIAM Journal on Matrix Analysis and Applications
publication_identifier:
eissn:
- 1095-7162
issn:
- 0895-4798
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the condition number of the shifted real Ginibre ensemble
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 43
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
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page: 3981-4002
publication: Annales Henri Poincaré
publication_identifier:
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issn:
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publication_status: published
publisher: Springer Nature
quality_controlled: '1'
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title: Density of small singular values of the shifted real Ginibre ensemble
tmp:
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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
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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
arxiv: 1
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
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- '530'
department:
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doi: 10.1063/5.0104290
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external_id:
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- '2206.04443'
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- '000869715800001'
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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
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success: 1
file_date_updated: 2023-01-30T08:01:10Z
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intvolume: ' 63'
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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'
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checksum: bb647b48fbdb59361210e425c220cdcb
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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
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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
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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: '8601'
abstract:
- lang: eng
text: We consider large non-Hermitian real or complex random matrices X with independent,
identically distributed centred entries. We prove that their local eigenvalue
statistics near the spectral edge, the unit circle, coincide with those of the
Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result
is the non-Hermitian counterpart of the universality of the Tracy–Widom distribution
at the spectral edges of the Wigner ensemble.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
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. Edge universality for non-Hermitian random
matrices. Probability Theory and Related Fields. 2021. doi:10.1007/s00440-020-01003-7
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Edge universality for
non-Hermitian random matrices. Probability Theory and Related Fields. Springer
Nature. https://doi.org/10.1007/s00440-020-01003-7
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Edge Universality
for Non-Hermitian Random Matrices.” Probability Theory and Related Fields.
Springer Nature, 2021. https://doi.org/10.1007/s00440-020-01003-7.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Edge universality for non-Hermitian
random matrices,” Probability Theory and Related Fields. Springer Nature,
2021.
ista: Cipolloni G, Erdös L, Schröder DJ. 2021. Edge universality for non-Hermitian
random matrices. Probability Theory and Related Fields.
mla: Cipolloni, Giorgio, et al. “Edge Universality for Non-Hermitian Random Matrices.”
Probability Theory and Related Fields, Springer Nature, 2021, doi:10.1007/s00440-020-01003-7.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields
(2021).
date_created: 2020-10-04T22:01:37Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2024-03-07T15:07:53Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00440-020-01003-7
ec_funded: 1
external_id:
arxiv:
- '1908.00969'
isi:
- '000572724600002'
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date_updated: 2020-10-05T14:53:40Z
file_id: '8612'
file_name: 2020_ProbTheory_Cipolloni.pdf
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relation: main_file
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file_date_updated: 2020-10-05T14:53:40Z
has_accepted_license: '1'
isi: 1
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- '14322064'
issn:
- '01788051'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Edge universality for non-Hermitian 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: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2021'
...