---
OA_place: publisher
OA_type: hybrid
_id: '15378'
abstract:
- lang: eng
text: We consider N×N non-Hermitian random matrices of the form X+A, where A is
a general deterministic matrix and N−−√X consists of independent entries with
zero mean, unit variance, and bounded densities. For this ensemble, we prove (i)
a Wegner estimate, i.e. that the local density of eigenvalues is bounded by N1+o(1)
and (ii) that the expected condition number of any bulk eigenvalue is bounded
by N1+o(1); both results are optimal up to the factor No(1). The latter result
complements the very recent matching lower bound obtained in [15] (arXiv:2301.03549)
and improves the N-dependence of the upper bounds in [5,6,32] (arXiv:1906.11819,
arXiv:2005.08930, arXiv:2005.08908). Our main ingredient, a near-optimal lower
tail estimate for the small singular values of X+A−z, is of independent interest.
acknowledgement: László Erdős is partially supported by ERC Advanced Grant “RMTBeyond”
No. 101020331. Hong Chang Ji is supported by ERC Advanced Grant “RMTBeyond” No.
101020331.
article_processing_charge: Yes (via OA deal)
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. Wegner estimate and upper bound on the eigenvalue condition
number of non-Hermitian random matrices. Communications on Pure and Applied
Mathematics. 2024;77(9):3785-3840. doi:10.1002/cpa.22201
apa: Erdös, L., & Ji, H. C. (2024). Wegner estimate and upper bound on the eigenvalue
condition number of non-Hermitian random matrices. Communications on Pure and
Applied Mathematics. Wiley. https://doi.org/10.1002/cpa.22201
chicago: Erdös, László, and Hong Chang Ji. “Wegner Estimate and Upper Bound on the
Eigenvalue Condition Number of Non-Hermitian Random Matrices.” Communications
on Pure and Applied Mathematics. Wiley, 2024. https://doi.org/10.1002/cpa.22201.
ieee: L. Erdös and H. C. Ji, “Wegner estimate and upper bound on the eigenvalue
condition number of non-Hermitian random matrices,” Communications on Pure
and Applied Mathematics, vol. 77, no. 9. Wiley, pp. 3785–3840, 2024.
ista: Erdös L, Ji HC. 2024. Wegner estimate and upper bound on the eigenvalue condition
number of non-Hermitian random matrices. Communications on Pure and Applied Mathematics.
77(9), 3785–3840.
mla: Erdös, László, and Hong Chang Ji. “Wegner Estimate and Upper Bound on the Eigenvalue
Condition Number of Non-Hermitian Random Matrices.” Communications on Pure
and Applied Mathematics, vol. 77, no. 9, Wiley, 2024, pp. 3785–840, doi:10.1002/cpa.22201.
short: L. Erdös, H.C. Ji, Communications on Pure and Applied Mathematics 77 (2024)
3785–3840.
corr_author: '1'
date_created: 2024-05-12T22:01:02Z
date_published: 2024-09-01T00:00:00Z
date_updated: 2025-09-08T07:25:47Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1002/cpa.22201
ec_funded: 1
external_id:
arxiv:
- '2301.04981'
isi:
- '001217139900001'
file:
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checksum: fbcc9cc7bf274f024e4f4afc9c208f96
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creator: dernst
date_created: 2025-01-09T09:36:41Z
date_updated: 2025-01-09T09:36:41Z
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has_accepted_license: '1'
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isi: 1
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month: '09'
oa: 1
oa_version: Published Version
page: 3785-3840
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
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: Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian
random matrices
tmp:
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legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
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(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: journal_article
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volume: 77
year: '2024'
...
---
_id: '17281'
abstract:
- lang: eng
text: We extend the free convolution of Brown measures of R-diagonal elements introduced
by Kösters and Tikhomirov [ 28] to fractional powers. We then show how this fractional
free convolution arises naturally when studying the roots of random polynomials
with independent coefficients under repeated differentiation. When the proportion
of derivatives to the degree approaches one, we establish central limit theorem-type
behavior and discuss stable distributions.
acknowledgement: This work was supported by the National Science Foundation [Grant
No. DMS-2143142 to S.O.]; and the European Research Council [Grant No. 101020331].The
third author acknowledges the support of the University of Colorado Boulder, where
a portion of this work was completed. The authors thank Martin Auer, Vadim Gorin,
Brian Hall, and Noah Williams for comments, corrections, and references. The authors
also wish to thank the anonymous referees for useful feedback and corrections.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Andrew J
full_name: Campbell, Andrew J
id: 582b06a9-1f1c-11ee-b076-82ffce00dde4
last_name: Campbell
- first_name: Sean
full_name: O'Rourke, Sean
last_name: O'Rourke
- first_name: David T
full_name: Renfrew, David T
id: 4845BF6A-F248-11E8-B48F-1D18A9856A87
last_name: Renfrew
orcid: 0000-0003-3493-121X
citation:
ama: Campbell AJ, O’Rourke S, Renfrew DT. The fractional free convolution of R-diagonal
elements and random polynomials under repeated differentiation. International
Mathematics Research Notices. 2024;2024(13):10189-10218. doi:10.1093/imrn/rnae062
apa: Campbell, A. J., O’Rourke, S., & Renfrew, D. T. (2024). The fractional
free convolution of R-diagonal elements and random polynomials under repeated
differentiation. International Mathematics Research Notices. Oxford University
Press. https://doi.org/10.1093/imrn/rnae062
chicago: Campbell, Andrew J, Sean O’Rourke, and David T Renfrew. “The Fractional
Free Convolution of R-Diagonal Elements and Random Polynomials under Repeated
Differentiation.” International Mathematics Research Notices. Oxford University
Press, 2024. https://doi.org/10.1093/imrn/rnae062.
ieee: A. J. Campbell, S. O’Rourke, and D. T. Renfrew, “The fractional free convolution
of R-diagonal elements and random polynomials under repeated differentiation,”
International Mathematics Research Notices, vol. 2024, no. 13. Oxford University
Press, pp. 10189–10218, 2024.
ista: Campbell AJ, O’Rourke S, Renfrew DT. 2024. The fractional free convolution
of R-diagonal elements and random polynomials under repeated differentiation.
International Mathematics Research Notices. 2024(13), 10189–10218.
mla: Campbell, Andrew J., et al. “The Fractional Free Convolution of R-Diagonal
Elements and Random Polynomials under Repeated Differentiation.” International
Mathematics Research Notices, vol. 2024, no. 13, Oxford University Press,
2024, pp. 10189–218, doi:10.1093/imrn/rnae062.
short: A.J. Campbell, S. O’Rourke, D.T. Renfrew, International Mathematics Research
Notices 2024 (2024) 10189–10218.
corr_author: '1'
date_created: 2024-07-21T22:01:01Z
date_published: 2024-07-01T00:00:00Z
date_updated: 2025-09-08T08:16:32Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1093/imrn/rnae062
external_id:
isi:
- '001198019500001'
file:
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checksum: f36a7dbf53f23d5833db711052e69b49
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creator: dernst
date_created: 2024-07-22T06:40:19Z
date_updated: 2024-07-22T06:40:19Z
file_id: '17288'
file_name: 2024_IMRN_Campbell.pdf
file_size: 1233508
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file_date_updated: 2024-07-22T06:40:19Z
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issue: '13'
language:
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license: https://creativecommons.org/licenses/by/4.0/
month: '07'
oa: 1
oa_version: Published Version
page: 10189-10218
publication: International Mathematics Research Notices
publication_identifier:
eissn:
- 1687-0247
issn:
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publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: The fractional free convolution of R-diagonal elements and random polynomials
under repeated differentiation
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 2024
year: '2024'
...
---
_id: '17375'
abstract:
- lang: eng
text: We consider the spectral radius of a large random matrix X with independent,
identically distributed entries. We show that its typical size is given by a precise
three-term asymptotics with an optimal error term beyond the radius of the celebrated
circular law. The coefficients in this asymptotics are universal but they differ
from a similar asymptotics recently proved for the rightmost eigenvalue of X in
Cipolloni et al., Ann. Probab. 51(6), 2192–2242 (2023). To access the more complicated
spectral radius, we need to establish a new decorrelation mechanism for the low-lying
singular values of X − z for different complex shift parameters z using the Dyson
Brownian Motion.
acknowledgement: L.E. and Y.X. were supported by the ERC Advanced Grant “RMTBeyond”
Grant No. 101020331.
article_number: '063302'
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: Yuanyuan
full_name: Xu, Yuanyuan
id: 7902bdb1-a2a4-11eb-a164-c9216f71aea3
last_name: Xu
orcid: 0000-0003-1559-1205
citation:
ama: Cipolloni G, Erdös L, Xu Y. Precise asymptotics for the spectral radius of
a large random matrix. Journal of Mathematical Physics. 2024;65(6). doi:10.1063/5.0209705
apa: Cipolloni, G., Erdös, L., & Xu, Y. (2024). Precise asymptotics for the
spectral radius of a large random matrix. Journal of Mathematical Physics.
AIP Publishing. https://doi.org/10.1063/5.0209705
chicago: Cipolloni, Giorgio, László Erdös, and Yuanyuan Xu. “Precise Asymptotics
for the Spectral Radius of a Large Random Matrix.” Journal of Mathematical
Physics. AIP Publishing, 2024. https://doi.org/10.1063/5.0209705.
ieee: G. Cipolloni, L. Erdös, and Y. Xu, “Precise asymptotics for the spectral radius
of a large random matrix,” Journal of Mathematical Physics, vol. 65, no.
6. AIP Publishing, 2024.
ista: Cipolloni G, Erdös L, Xu Y. 2024. Precise asymptotics for the spectral radius
of a large random matrix. Journal of Mathematical Physics. 65(6), 063302.
mla: Cipolloni, Giorgio, et al. “Precise Asymptotics for the Spectral Radius of
a Large Random Matrix.” Journal of Mathematical Physics, vol. 65, no. 6,
063302, AIP Publishing, 2024, doi:10.1063/5.0209705.
short: G. Cipolloni, L. Erdös, Y. Xu, Journal of Mathematical Physics 65 (2024).
corr_author: '1'
date_created: 2024-08-04T22:01:22Z
date_published: 2024-06-01T00:00:00Z
date_updated: 2025-09-08T08:44:57Z
day: '01'
department:
- _id: LaEr
doi: 10.1063/5.0209705
ec_funded: 1
external_id:
arxiv:
- '2210.15643'
isi:
- '001252240700002'
intvolume: ' 65'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2210.15643
month: '06'
oa: 1
oa_version: Preprint
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Journal of Mathematical Physics
publication_identifier:
issn:
- 0022-2488
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Precise asymptotics for the spectral radius of a large random matrix
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 65
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '18554'
abstract:
- lang: eng
text: We prove the Eigenstate Thermalization Hypothesis for general Wigner-type
matrices in the bulk of the self-consistent spectrum, with optimal control on
the fluctuations for obs ervables of arbitrary rank. As the main technical ingredient,
we prove rank-uniform optimal local laws for one and two resolvents of a Wigner-type
matrix with regular observables. Our results hold under very general conditions
on the variance profile, even allowing many vanishing entries, demonstrating that
Eigenstate Thermalization occurs robustly across a diverse class of random matrix
ensembles, for which the underlying quantum system has a non-trivial spatial structure.
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria).
article_number: '282'
article_processing_charge: Yes (via OA deal)
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: Volodymyr
full_name: Riabov, Volodymyr
id: 1949f904-edfb-11eb-afb5-e2dfddabb93b
last_name: Riabov
citation:
ama: Erdös L, Riabov V. Eigenstate Thermalization Hypothesis for Wigner-type matrices.
Communications in Mathematical Physics. 2024;405(12). doi:10.1007/s00220-024-05143-y
apa: Erdös, L., & Riabov, V. (2024). Eigenstate Thermalization Hypothesis for
Wigner-type matrices. Communications in Mathematical Physics. Springer
Nature. https://doi.org/10.1007/s00220-024-05143-y
chicago: Erdös, László, and Volodymyr Riabov. “Eigenstate Thermalization Hypothesis
for Wigner-Type Matrices.” Communications in Mathematical Physics. Springer
Nature, 2024. https://doi.org/10.1007/s00220-024-05143-y.
ieee: L. Erdös and V. Riabov, “Eigenstate Thermalization Hypothesis for Wigner-type
matrices,” Communications in Mathematical Physics, vol. 405, no. 12. Springer
Nature, 2024.
ista: Erdös L, Riabov V. 2024. Eigenstate Thermalization Hypothesis for Wigner-type
matrices. Communications in Mathematical Physics. 405(12), 282.
mla: Erdös, László, and Volodymyr Riabov. “Eigenstate Thermalization Hypothesis
for Wigner-Type Matrices.” Communications in Mathematical Physics, vol.
405, no. 12, 282, Springer Nature, 2024, doi:10.1007/s00220-024-05143-y.
short: L. Erdös, V. Riabov, Communications in Mathematical Physics 405 (2024).
corr_author: '1'
date_created: 2024-11-17T23:01:46Z
date_published: 2024-12-01T00:00:00Z
date_updated: 2026-04-07T12:32:19Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00220-024-05143-y
external_id:
arxiv:
- '2403.10359'
isi:
- '001348943900004'
pmid:
- '39526190'
file:
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checksum: c9ae0ea195bd39b8b3a630d492fb00dc
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publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
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publisher: Springer Nature
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scopus_import: '1'
status: public
title: Eigenstate Thermalization Hypothesis for Wigner-type 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)
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type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 405
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '18656'
abstract:
- lang: eng
text: "We consider the time evolution of the out-of-time-ordered correlator (OTOC)
of two general observables \r\n and \r\n in a mean field chaotic quantum system
described by a random Wigner matrix as its Hamiltonian. We rigorously identify
three time regimes separated by the physically relevant scrambling and relaxation
times. The main feature of our analysis is that we express the error terms in
the optimal Schatten (tracial) norms of the observables, allowing us to track
the exact dependence of the errors on their rank. In particular, for significantly
overlapping observables with low rank the OTOC is shown to exhibit a significant
local maximum at the scrambling time, a feature that may not have been noticed
in the physics literature before. Our main tool is a novel multi-resolvent local
law with Schatten norms that unifies and improves previous local laws involving
either the much cruder operator norm (cf. [10]) or the Hilbert-Schmidt norm (cf.
[11])."
acknowledgement: LE and JH were supported by the ERC Advanced Grant łRMTBeyondž No.
101020331
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: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
citation:
ama: Cipolloni G, Erdös L, Henheik SJ. Out-of-time-ordered correlators for Wigner
matrices. Advances in Theoretical and Mathematical Physics. 2024;28(6):2025-2083.
doi:10.4310/ATMP.241031013250
apa: Cipolloni, G., Erdös, L., & Henheik, S. J. (2024). Out-of-time-ordered
correlators for Wigner matrices. Advances in Theoretical and Mathematical Physics.
International Press. https://doi.org/10.4310/ATMP.241031013250
chicago: Cipolloni, Giorgio, László Erdös, and Sven Joscha Henheik. “Out-of-Time-Ordered
Correlators for Wigner Matrices.” Advances in Theoretical and Mathematical
Physics. International Press, 2024. https://doi.org/10.4310/ATMP.241031013250.
ieee: G. Cipolloni, L. Erdös, and S. J. Henheik, “Out-of-time-ordered correlators
for Wigner matrices,” Advances in Theoretical and Mathematical Physics,
vol. 28, no. 6. International Press, pp. 2025–2083, 2024.
ista: Cipolloni G, Erdös L, Henheik SJ. 2024. Out-of-time-ordered correlators for
Wigner matrices. Advances in Theoretical and Mathematical Physics. 28(6), 2025–2083.
mla: Cipolloni, Giorgio, et al. “Out-of-Time-Ordered Correlators for Wigner Matrices.”
Advances in Theoretical and Mathematical Physics, vol. 28, no. 6, International
Press, 2024, pp. 2025–83, doi:10.4310/ATMP.241031013250.
short: G. Cipolloni, L. Erdös, S.J. Henheik, Advances in Theoretical and Mathematical
Physics 28 (2024) 2025–2083.
corr_author: '1'
date_created: 2024-12-15T23:01:51Z
date_published: 2024-10-30T00:00:00Z
date_updated: 2026-04-07T12:37:10Z
day: '30'
department:
- _id: LaEr
doi: 10.4310/ATMP.241031013250
ec_funded: 1
external_id:
arxiv:
- '2402.17609'
intvolume: ' 28'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2402.17609
month: '10'
oa: 1
oa_version: Preprint
page: 2025-2083
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Advances in Theoretical and Mathematical Physics
publication_identifier:
eissn:
- 1095-0753
issn:
- 1095-0761
publication_status: published
publisher: International Press
quality_controlled: '1'
related_material:
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scopus_import: '1'
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title: Out-of-time-ordered correlators for Wigner matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '17049'
abstract:
- lang: eng
text: We consider large non-Hermitian NxN matrices with an additive independent,
identically distributed (i.i.d.) noise for each matrix elements. We show that
already a small noise of variance 1/N completely thermalises the bulk singular
vectors, in particular they satisfy the strong form of Quantum Unique Ergodicity
(QUE) with an optimal speed of convergence. In physics terms, we thus extend the
Eigenstate Thermalisation Hypothesis, formulated originally by Deutsch [34] and
proven for Wigner matrices in [23], to arbitrary non-Hermitian matrices with an
i.i.d. noise. As a consequence we obtain an optimal lower bound on the diagonal
overlaps of the corresponding non-Hermitian eigenvectors. This quantity, also
known as the (square of the) eigenvalue condition number measuring the sensitivity
of the eigenvalue to small perturbations, has notoriously escaped rigorous treatment
beyond the explicitly computable Ginibre ensemble apart from the very recent upper
bounds given in [7] and [45]. As a key tool, we develop a new systematic decomposition
of general observables in random matrix theory that governs the size of products
of resolvents with deterministic matrices in between.
acknowledgement: "Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nSupported
by the SNSF Ambizione Grant PZ00P2_209089."
article_number: '110495'
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: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- 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, Henheik SJ, Schröder DJ. Optimal lower bound on eigenvector
overlaps for non-Hermitian random matrices. Journal of Functional Analysis.
2024;287(4). doi:10.1016/j.jfa.2024.110495
apa: Cipolloni, G., Erdös, L., Henheik, S. J., & Schröder, D. J. (2024). Optimal
lower bound on eigenvector overlaps for non-Hermitian random matrices. Journal
of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2024.110495
chicago: Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Dominik J Schröder.
“Optimal Lower Bound on Eigenvector Overlaps for Non-Hermitian Random Matrices.”
Journal of Functional Analysis. Elsevier, 2024. https://doi.org/10.1016/j.jfa.2024.110495.
ieee: G. Cipolloni, L. Erdös, S. J. Henheik, and D. J. Schröder, “Optimal lower
bound on eigenvector overlaps for non-Hermitian random matrices,” Journal of
Functional Analysis, vol. 287, no. 4. Elsevier, 2024.
ista: Cipolloni G, Erdös L, Henheik SJ, Schröder DJ. 2024. Optimal lower bound on
eigenvector overlaps for non-Hermitian random matrices. Journal of Functional
Analysis. 287(4), 110495.
mla: Cipolloni, Giorgio, et al. “Optimal Lower Bound on Eigenvector Overlaps for
Non-Hermitian Random Matrices.” Journal of Functional Analysis, vol. 287,
no. 4, 110495, Elsevier, 2024, doi:10.1016/j.jfa.2024.110495.
short: G. Cipolloni, L. Erdös, S.J. Henheik, D.J. Schröder, Journal of Functional
Analysis 287 (2024).
corr_author: '1'
date_created: 2024-05-26T22:00:57Z
date_published: 2024-08-15T00:00:00Z
date_updated: 2026-04-07T12:37:11Z
day: '15'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1016/j.jfa.2024.110495
ec_funded: 1
external_id:
isi:
- '001325502400001'
file:
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checksum: 07d3f73e0c56e68eb110851842c22ee0
content_type: application/pdf
creator: dernst
date_created: 2025-06-24T13:14:21Z
date_updated: 2025-06-24T13:14:21Z
file_id: '19891'
file_name: 2025_JourFunctionalAnalysis_Cipolloni.pdf
file_size: 1374854
relation: main_file
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intvolume: ' 287'
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issue: '4'
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: Journal of Functional Analysis
publication_identifier:
eissn:
- 1096-0783
issn:
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publisher: Elsevier
quality_controlled: '1'
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status: public
title: Optimal lower bound on eigenvector overlaps 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 287
year: '2024'
...
---
OA_place: repository
_id: '19545'
abstract:
- lang: eng
text: "We prove the Eigenstate Thermalisation Hypothesis for Wigner matrices\r\nuniformly
in the entire spectrum, in particular near the spectral edges, with a\r\nbound
on the fluctuation that is optimal for any observable. This complements\r\nearlier
works of Cipolloni et. al. (Comm. Math. Phys. 388, 2021; Forum Math.,\r\nSigma
10, 2022) and Benigni et. al. (Comm. Math. Phys. 391, 2022; arXiv:\r\n2303.11142)
that were restricted either to the bulk of the spectrum or to\r\nspecial observables.
As a main ingredient, we prove a new multi-resolvent local\r\nlaw that optimally
accounts for the edge scaling."
acknowledgement: Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.
article_processing_charge: No
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
citation:
ama: Cipolloni G, Erdös L, Henheik SJ. Eigenstate thermalisation at the edge for
Wigner matrices. arXiv. doi:10.48550/arXiv.2309.05488
apa: Cipolloni, G., Erdös, L., & Henheik, S. J. (n.d.). Eigenstate thermalisation
at the edge for Wigner matrices. arXiv. https://doi.org/10.48550/arXiv.2309.05488
chicago: Cipolloni, Giorgio, László Erdös, and Sven Joscha Henheik. “Eigenstate
Thermalisation at the Edge for Wigner Matrices.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2309.05488.
ieee: G. Cipolloni, L. Erdös, and S. J. Henheik, “Eigenstate thermalisation at the
edge for Wigner matrices,” arXiv. .
ista: Cipolloni G, Erdös L, Henheik SJ. Eigenstate thermalisation at the edge for
Wigner matrices. arXiv, 10.48550/arXiv.2309.05488.
mla: Cipolloni, Giorgio, et al. “Eigenstate Thermalisation at the Edge for Wigner
Matrices.” ArXiv, doi:10.48550/arXiv.2309.05488.
short: G. Cipolloni, L. Erdös, S.J. Henheik, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-04-11T08:19:22Z
date_published: 2024-12-17T00:00:00Z
date_updated: 2026-04-07T12:37:11Z
day: '17'
department:
- _id: LaEr
doi: 10.48550/arXiv.2309.05488
ec_funded: 1
external_id:
arxiv:
- '2309.05488'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2309.05488
month: '12'
oa: 1
oa_version: Preprint
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: arXiv
publication_status: draft
related_material:
record:
- id: '19540'
relation: dissertation_contains
status: public
status: public
title: Eigenstate thermalisation at the edge 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: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2024'
...
---
OA_place: repository
_id: '19551'
abstract:
- lang: eng
text: "We introduce a notion of a \\emph{local gap} for interacting many-body quantum
lattice systems and prove the validity of response theory and Kubo's formula for
localized perturbations in such settings.\r\nOn a high level, our result shows
that the usual spectral gap condition, concerning the system as a whole, is not
a necessary condition for understanding local properties of the system.\r\nMore
precisely, we say that an equilibrium state ρ0 of a Hamiltonian H0 is locally
gapped in Λgap⊂Λ, whenever the Liouvillian −i[H0,⋅] is almost invertible on local
observables supported in Λgap when tested in ρ0.\r\nTo put this into context,
we provide other alternative notions of a local gap and discuss their relations.\r\nThe
validity of response theory is based on the construction of \\emph{non-equilibrium
almost stationary states} (NEASSs).\r\nBy controlling locality properties of the
NEASS construction, we show that response theory holds to any order, whenever
the perturbation \\(\\epsilon V\\) acts in a region which is further than |logϵ|
away from the non-gapped region Λ∖Λgap."
article_processing_charge: No
arxiv: 1
author:
- first_name: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- first_name: Tom
full_name: Wessel, Tom
last_name: Wessel
citation:
ama: Henheik SJ, Wessel T. Response theory for locally gapped systems. arXiv.
doi:10.48550/arXiv.2410.10809
apa: Henheik, S. J., & Wessel, T. (n.d.). Response theory for locally gapped
systems. arXiv. https://doi.org/10.48550/arXiv.2410.10809
chicago: Henheik, Sven Joscha, and Tom Wessel. “Response Theory for Locally Gapped
Systems.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2410.10809.
ieee: S. J. Henheik and T. Wessel, “Response theory for locally gapped systems,”
arXiv. .
ista: Henheik SJ, Wessel T. Response theory for locally gapped systems. arXiv, 10.48550/arXiv.2410.10809.
mla: Henheik, Sven Joscha, and Tom Wessel. “Response Theory for Locally Gapped Systems.”
ArXiv, doi:10.48550/arXiv.2410.10809.
short: S.J. Henheik, T. Wessel, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-04-11T11:54:56Z
date_published: 2024-10-14T00:00:00Z
date_updated: 2026-04-07T12:37:11Z
day: '14'
department:
- _id: LaEr
doi: 10.48550/arXiv.2410.10809
external_id:
arxiv:
- '2410.10809'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2410.10809
month: '10'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: draft
related_material:
record:
- id: '19540'
relation: dissertation_contains
status: public
status: public
title: Response theory for locally gapped 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: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2024'
...
---
OA_place: repository
_id: '19550'
abstract:
- lang: eng
text: "We introduce a multi-band BCS free energy functional and prove that for a\r\nmulti-band
superconductor the effect of inter-band coupling can only increase\r\nthe critical
temperature, irrespective of its attractive or repulsive nature\r\nand its strength.
Further, for weak coupling and weaker inter-band coupling, we\r\nprove that the
dependence of the increase in critical temperature on the\r\ninter-band coupling
is (1) linear, if there are two or more equally strongly\r\nsuperconducting bands,
or (2) quadratic, if there is only one dominating band."
article_processing_charge: No
arxiv: 1
author:
- first_name: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- first_name: Edwin
full_name: Langmann, Edwin
last_name: Langmann
- first_name: Asbjørn Bækgaard
full_name: Lauritsen, Asbjørn Bækgaard
id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1
last_name: Lauritsen
orcid: 0000-0003-4476-2288
citation:
ama: Henheik SJ, Langmann E, Lauritsen AB. Multi-band superconductors have enhanced
critical temperatures. arXiv. doi:10.48550/arXiv.2409.17297
apa: Henheik, S. J., Langmann, E., & Lauritsen, A. B. (n.d.). Multi-band superconductors
have enhanced critical temperatures. arXiv. https://doi.org/10.48550/arXiv.2409.17297
chicago: Henheik, Sven Joscha, Edwin Langmann, and Asbjørn Bækgaard Lauritsen. “Multi-Band
Superconductors Have Enhanced Critical Temperatures.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2409.17297.
ieee: S. J. Henheik, E. Langmann, and A. B. Lauritsen, “Multi-band superconductors
have enhanced critical temperatures,” arXiv. .
ista: Henheik SJ, Langmann E, Lauritsen AB. Multi-band superconductors have enhanced
critical temperatures. arXiv, 10.48550/arXiv.2409.17297.
mla: Henheik, Sven Joscha, et al. “Multi-Band Superconductors Have Enhanced Critical
Temperatures.” ArXiv, doi:10.48550/arXiv.2409.17297.
short: S.J. Henheik, E. Langmann, A.B. Lauritsen, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-04-11T11:43:58Z
date_published: 2024-10-21T00:00:00Z
date_updated: 2026-04-07T12:37:11Z
day: '21'
department:
- _id: LaEr
- _id: RoSe
doi: 10.48550/arXiv.2409.17297
external_id:
arxiv:
- '2409.17297'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2409.17297
month: '10'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: draft
related_material:
record:
- id: '19540'
relation: dissertation_contains
status: public
status: public
title: Multi-band superconductors have enhanced critical temperatures
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: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2024'
...
---
OA_place: repository
_id: '19547'
abstract:
- lang: eng
text: "For correlated real symmetric or complex Hermitian random matrices, we prove\r\nthat
the local eigenvalue statistics at any cusp singularity are universal.\r\nSince
the density of states typically exhibits only square root edge or cubic\r\nroot
cusp singularities, our result completes the proof of the\r\nWigner-Dyson-Mehta
universality conjecture in all spectral regimes for a very\r\ngeneral class of
random matrices. Previously only the bulk and the edge\r\nuniversality were established
in this generality [arXiv:1804.07744], while cusp\r\nuniversality was proven only
for Wigner-type matrices with independent entries\r\n[arXiv:1809.03971, arXiv:1811.04055].
As our main technical input, we prove an\r\noptimal local law at the cusp using
the Zigzag strategy, a recursive tandem of\r\nthe characteristic flow method and
a Green function comparison argument.\r\nMoreover, our proof of the optimal local
law holds uniformly in the spectrum,\r\nthus also re-establishing universality
of the local eigenvalue statistics in\r\nthe previously studied bulk [arXiv:1705.10661]
and edge [arXiv:1804.07744]\r\nregimes."
acknowledgement: "Supported by the ERC Advanced Grant \"RMTBeyond\"\r\nNo. 101020331."
article_processing_charge: No
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: 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
citation:
ama: Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices.
arXiv. doi:10.48550/arXiv.2410.06813
apa: Erdös, L., Henheik, S. J., & Riabov, V. (n.d.). Cusp universality for correlated
random matrices. arXiv. https://doi.org/10.48550/arXiv.2410.06813
chicago: Erdös, László, Sven Joscha Henheik, and Volodymyr Riabov. “Cusp Universality
for Correlated Random Matrices.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2410.06813.
ieee: L. Erdös, S. J. Henheik, and V. Riabov, “Cusp universality for correlated
random matrices,” arXiv. .
ista: Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices.
arXiv, 10.48550/arXiv.2410.06813.
mla: Erdös, László, et al. “Cusp Universality for Correlated Random Matrices.” ArXiv,
doi:10.48550/arXiv.2410.06813.
short: L. Erdös, S.J. Henheik, V. Riabov, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-04-11T08:48:21Z
date_published: 2024-11-03T00:00:00Z
date_updated: 2026-04-07T12:37:11Z
day: '03'
department:
- _id: LaEr
doi: 10.48550/arXiv.2410.06813
ec_funded: 1
external_id:
arxiv:
- '2410.06813'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2410.06813
month: '11'
oa: 1
oa_version: Preprint
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: arXiv
publication_status: draft
related_material:
record:
- id: '20322'
relation: later_version
status: public
- id: '20575'
relation: dissertation_contains
status: public
- id: '19540'
relation: dissertation_contains
status: public
status: public
title: Cusp universality for correlated random matrices
type: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '14542'
abstract:
- lang: eng
text: "It is a remarkable property of BCS theory that the ratio of the energy gap
at zero temperature Ξ\r\n and the critical temperature Tc is (approximately) given
by a universal constant, independent of the microscopic details of the fermionic
interaction. This universality has rigorously been proven quite recently in three
spatial dimensions and three different limiting regimes: weak coupling, low density
and high density. The goal of this short note is to extend the universal behavior
to lower dimensions d=1,2 and give an exemplary proof in the weak coupling limit."
acknowledgement: We thank Robert Seiringer for comments on the paper. J. H. gratefully
acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond”No.
101020331.This research was funded in part by the Austrian Science Fund (FWF) grantnumber
I6427.
article_number: '2360005 '
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- first_name: Asbjørn Bækgaard
full_name: Lauritsen, Asbjørn Bækgaard
id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1
last_name: Lauritsen
orcid: 0000-0003-4476-2288
- first_name: Barbara
full_name: Roos, Barbara
id: 5DA90512-D80F-11E9-8994-2E2EE6697425
last_name: Roos
orcid: 0000-0002-9071-5880
citation:
ama: Henheik SJ, Lauritsen AB, Roos B. Universality in low-dimensional BCS theory.
Reviews in Mathematical Physics. 2024;36(9). doi:10.1142/s0129055x2360005x
apa: Henheik, S. J., Lauritsen, A. B., & Roos, B. (2024). Universality in low-dimensional
BCS theory. Reviews in Mathematical Physics. World Scientific Publishing.
https://doi.org/10.1142/s0129055x2360005x
chicago: Henheik, Sven Joscha, Asbjørn Bækgaard Lauritsen, and Barbara Roos. “Universality
in Low-Dimensional BCS Theory.” Reviews in Mathematical Physics. World
Scientific Publishing, 2024. https://doi.org/10.1142/s0129055x2360005x.
ieee: S. J. Henheik, A. B. Lauritsen, and B. Roos, “Universality in low-dimensional
BCS theory,” Reviews in Mathematical Physics, vol. 36, no. 9. World Scientific
Publishing, 2024.
ista: Henheik SJ, Lauritsen AB, Roos B. 2024. Universality in low-dimensional BCS
theory. Reviews in Mathematical Physics. 36(9), 2360005.
mla: Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.”
Reviews in Mathematical Physics, vol. 36, no. 9, 2360005, World Scientific
Publishing, 2024, doi:10.1142/s0129055x2360005x.
short: S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics 36
(2024).
corr_author: '1'
date_created: 2023-11-15T23:48:14Z
date_published: 2024-10-01T00:00:00Z
date_updated: 2026-04-07T13:01:40Z
day: '01'
ddc:
- '510'
department:
- _id: GradSch
- _id: LaEr
- _id: RoSe
doi: 10.1142/s0129055x2360005x
ec_funded: 1
external_id:
arxiv:
- '2301.05621'
isi:
- '001099640300002'
file:
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checksum: 2b053a4223b4db14b90520999ec56054
content_type: application/pdf
creator: dernst
date_created: 2025-01-09T07:56:28Z
date_updated: 2025-01-09T07:56:28Z
file_id: '18786'
file_name: 2024_ReviewsmathPhysics_Henheik.pdf
file_size: 503910
relation: main_file
success: 1
file_date_updated: 2025-01-09T07:56:28Z
has_accepted_license: '1'
intvolume: ' 36'
isi: 1
issue: '9'
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
- _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b
grant_number: I06427
name: Mathematical Challenges in BCS Theory of Superconductivity
publication: Reviews in Mathematical Physics
publication_identifier:
eissn:
- 1793-6659
issn:
- 0129-055X
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
related_material:
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- id: '19540'
relation: dissertation_contains
status: public
- id: '18135'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Universality in low-dimensional BCS theory
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: 36
year: '2024'
...
---
OA_place: publisher
_id: '17164'
abstract:
- lang: eng
text: "This thesis is structured into two parts. In the first part, we consider
the random\r\nvariable X := Tr(f1(W)A1 . . . fk(W)Ak) where W is an N × N Hermitian
Wigner matrix, k ∈ N, and we choose (possibly N-dependent) regular functions f1,
. . . , fk as well as\r\nbounded deterministic matrices A1, . . . , Ak. In this
context, we prove a functional central\r\nlimit theorem on macroscopic and mesoscopic
scales, showing that the fluctuations of X\r\naround its expectation are Gaussian
and that the limiting covariance structure is given\r\nby a deterministic recursion.
We further give explicit error bounds in terms of the scaling\r\nof f1, . . .
, fk and the number of traceless matrices among A1, . . . , Ak, thus extending\r\nthe
results of Cipolloni, Erdős and Schröder [40] to products of arbitrary length
k ≥ 2.\r\nAnalyzing the underlying combinatorics leads to a non-recursive formula
for the variance\r\nof X as well as the covariance of X and Y := Tr(fk+1(W)Ak+1
. . . fk+ℓ(W)Ak+ℓ) of similar\r\nbuild. When restricted to polynomials, these
formulas reproduce recent results of Male,\r\nMingo, Peché, and Speicher [107],
showing that the underlying combinatorics of noncrossing partitions and annular
non-crossing permutations continue to stay valid beyond\r\nthe setting of second-order
free probability theory. As an application, we consider the\r\nfluctuation of
Tr(eitW A1e\r\n−itW A2)/N around its thermal value Tr(A1) Tr(A2)/N2 when t\r\nis
large and give an explicit formula for the variance.\r\nThe second part of the
thesis collects three smaller projects focusing on different random\r\nmatrix
models. In the first project, we show that a class of weakly perturbed Hamiltonians\r\nof
the form Hλ = H0 + λW, where W is a Wigner matrix, exhibits prethermalization.\r\nThat
is, the time evolution generated by Hλ relaxes to its ultimate thermal state via
an\r\nintermediate prethermal state with a lifetime of order λ\r\n−2\r\n. As the
main result, we obtain\r\na general relaxation formula, expressing the perturbed
dynamics via the unperturbed\r\ndynamics and the ultimate thermal state. The proof
relies on a two-resolvent global law\r\nfor the deformed Wigner matrix Hλ.\r\nThe
second project focuses on correlated random matrices, more precisely on a correlated
N × N Hermitian random matrix with a polynomially decaying metric correlation\r\nstructure.
A trivial a priori bound shows that the operator norm of this model is stochastically
dominated by √\r\nN. However, by calculating the trace of the moments of the matrix\r\nand
using the summable decay of the cumulants, the norm estimate can be improved to
a\r\nbound of order one.\r\nIn the third project, we consider a multiplicative
perturbation of the form UA(t) where U\r\nis a unitary random matrix and A = diag(t,
1, ..., 1). This so-called UA model was\r\nfirst introduced by Fyodorov [73] for
its applications in scattering theory. We give a\r\ngeneral description of the
eigenvalue trajectories obtained by varying the parameter t and\r\nintroduce a
flow of deterministic domains that separates the outlier resulting from the\r\nrank-one
perturbation from the typical eigenvalues for all sub-critical timescales. The\r\nresults
are obtained under generic assumptions on U that hold for various unitary random\r\nmatrices,
including the circular unitary ensemble (CUE) in the original formulation of\r\nthe
model."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Jana
full_name: Reker, Jana
id: e796e4f9-dc8d-11ea-abe3-97e26a0323e9
last_name: Reker
citation:
ama: 'Reker J. Central limit theorems for random matrices: From resolvents to free
probability. 2024. doi:10.15479/at:ista:17164'
apa: 'Reker, J. (2024). Central limit theorems for random matrices: From resolvents
to free probability. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:17164'
chicago: 'Reker, Jana. “Central Limit Theorems for Random Matrices: From Resolvents
to Free Probability.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:17164.'
ieee: 'J. Reker, “Central limit theorems for random matrices: From resolvents to
free probability,” Institute of Science and Technology Austria, 2024.'
ista: 'Reker J. 2024. Central limit theorems for random matrices: From resolvents
to free probability. Institute of Science and Technology Austria.'
mla: 'Reker, Jana. Central Limit Theorems for Random Matrices: From Resolvents
to Free Probability. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:17164.'
short: 'J. Reker, Central Limit Theorems for Random Matrices: From Resolvents to
Free Probability, Institute of Science and Technology Austria, 2024.'
corr_author: '1'
date_created: 2024-06-24T11:23:29Z
date_published: 2024-06-26T00:00:00Z
date_updated: 2026-04-07T13:02:13Z
day: '26'
ddc:
- '519'
degree_awarded: PhD
department:
- _id: GradSch
- _id: LaEr
doi: 10.15479/at:ista:17164
ec_funded: 1
file:
- access_level: open_access
checksum: fb16d86e1f2753dc3a9e14d2bdfd84cd
content_type: application/pdf
creator: jreker
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file_name: ISTA_Thesis_JReker.pdf
file_size: 2783027
relation: main_file
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creator: jreker
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file_name: ISTA_Thesis_JReker_SourceFiles.zip
file_size: 3054878
relation: source_file
file_date_updated: 2024-06-26T12:44:53Z
has_accepted_license: '1'
keyword:
- Random Matrices
- Spectrum
- Central Limit Theorem
- Resolvent
- Free Probability
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-sa/4.0/
month: '06'
oa: 1
oa_version: Published Version
page: '206'
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
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status: public
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- id: '17154'
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status: public
- id: '17174'
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status: public
status: public
supervisor:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
title: 'Central limit theorems for random matrices: From resolvents to free probability'
tmp:
image: /images/cc_by_nc_sa.png
legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC
BY-NC-SA 4.0)
short: CC BY-NC-SA (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2024'
...
---
_id: '17154'
abstract:
- lang: eng
text: We compute the deterministic approximation for mixed fluctuation moments of
products of deterministic matrices and general Sobolev functions of Wigner matrices.
Restricting to polynomials, our formulas reproduce recent results of Male et al.
(Random Matrices Theory Appl. 11(2):2250015, 2022), showing that the underlying
combinatorics of non-crossing partitions and annular non-crossing permutations
continue to stay valid beyond the setting of second-order free probability theory.
The formulas obtained further characterize the variance in the functional central
limit theorem given in the recent companion paper (Reker in Preprint, arXiv:2204.03419,
2023). and thus allow identifying the fluctuation around the thermal value in
certain thermalization problems.
article_number: '10'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Jana
full_name: Reker, Jana
id: e796e4f9-dc8d-11ea-abe3-97e26a0323e9
last_name: Reker
citation:
ama: Reker J. Fluctuation moments for regular functions of Wigner Matrices. Mathematical
Physics, Analysis and Geometry. 2024;27(3). doi:10.1007/s11040-024-09483-y
apa: Reker, J. (2024). Fluctuation moments for regular functions of Wigner Matrices.
Mathematical Physics, Analysis and Geometry. Springer Nature. https://doi.org/10.1007/s11040-024-09483-y
chicago: Reker, Jana. “Fluctuation Moments for Regular Functions of Wigner Matrices.”
Mathematical Physics, Analysis and Geometry. Springer Nature, 2024. https://doi.org/10.1007/s11040-024-09483-y.
ieee: J. Reker, “Fluctuation moments for regular functions of Wigner Matrices,”
Mathematical Physics, Analysis and Geometry, vol. 27, no. 3. Springer Nature,
2024.
ista: Reker J. 2024. Fluctuation moments for regular functions of Wigner Matrices.
Mathematical Physics, Analysis and Geometry. 27(3), 10.
mla: Reker, Jana. “Fluctuation Moments for Regular Functions of Wigner Matrices.”
Mathematical Physics, Analysis and Geometry, vol. 27, no. 3, 10, Springer
Nature, 2024, doi:10.1007/s11040-024-09483-y.
short: J. Reker, Mathematical Physics, Analysis and Geometry 27 (2024).
date_created: 2024-06-21T09:31:17Z
date_published: 2024-06-20T00:00:00Z
date_updated: 2026-04-07T13:02:12Z
day: '20'
ddc:
- '519'
department:
- _id: LaEr
doi: 10.1007/s11040-024-09483-y
ec_funded: 1
external_id:
arxiv:
- '2307.11029'
isi:
- '001251464300001'
file:
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checksum: 7d04318d66f765621bdcb648378d458e
content_type: application/pdf
creator: cchlebak
date_created: 2024-06-26T11:26:42Z
date_updated: 2024-06-26T11:26:42Z
file_id: '17175'
file_name: 2024_MathPhysAnaGeo_Reker.pdf
file_size: 1327596
relation: main_file
success: 1
file_date_updated: 2024-06-26T11:26:42Z
has_accepted_license: '1'
intvolume: ' 27'
isi: 1
issue: '3'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Mathematical Physics, Analysis and Geometry
publication_identifier:
eissn:
- 1572-9656
issn:
- 1385-0172
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '17164'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Fluctuation moments for regular functions of 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 27
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '17047'
abstract:
- lang: eng
text: We provide a dynamical study of a model of multiplicative perturbation of
a unitary matrix introduced by Fyodorov. In particular, we identify a flow of
deterministic domains that bound the spectrum with high probability, separating
the outlier from the typical eigenvalues at all sub-critical timescales. These
results are obtained under generic assumptions on U that hold for a variety of
unitary random matrix models.
article_number: '2450007'
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: Jana
full_name: Reker, Jana
id: e796e4f9-dc8d-11ea-abe3-97e26a0323e9
last_name: Reker
citation:
ama: 'Dubach G, Reker J. Dynamics of a rank-one multiplicative perturbation of a
unitary matrix. Random Matrices: Theory and Applications. 2024;13(2). doi:10.1142/s2010326324500072'
apa: 'Dubach, G., & Reker, J. (2024). Dynamics of a rank-one multiplicative
perturbation of a unitary matrix. Random Matrices: Theory and Applications.
World Scientific Publishing. https://doi.org/10.1142/s2010326324500072'
chicago: 'Dubach, Guillaume, and Jana Reker. “Dynamics of a Rank-One Multiplicative
Perturbation of a Unitary Matrix.” Random Matrices: Theory and Applications.
World Scientific Publishing, 2024. https://doi.org/10.1142/s2010326324500072.'
ieee: 'G. Dubach and J. Reker, “Dynamics of a rank-one multiplicative perturbation
of a unitary matrix,” Random Matrices: Theory and Applications, vol. 13,
no. 2. World Scientific Publishing, 2024.'
ista: 'Dubach G, Reker J. 2024. Dynamics of a rank-one multiplicative perturbation
of a unitary matrix. Random Matrices: Theory and Applications. 13(2), 2450007.'
mla: 'Dubach, Guillaume, and Jana Reker. “Dynamics of a Rank-One Multiplicative
Perturbation of a Unitary Matrix.” Random Matrices: Theory and Applications,
vol. 13, no. 2, 2450007, World Scientific Publishing, 2024, doi:10.1142/s2010326324500072.'
short: 'G. Dubach, J. Reker, Random Matrices: Theory and Applications 13 (2024).'
corr_author: '1'
date_created: 2024-05-23T08:31:57Z
date_published: 2024-04-01T00:00:00Z
date_updated: 2026-04-07T13:02:12Z
day: '01'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1142/s2010326324500072
ec_funded: 1
external_id:
arxiv:
- '2212.14638'
isi:
- '001229295200002'
intvolume: ' 13'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2212.14638'
month: '04'
oa: 1
oa_version: Preprint
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: 'Random Matrices: Theory and Applications'
publication_identifier:
eissn:
- 2010-3271
issn:
- 2010-3263
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
related_material:
record:
- id: '17164'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Dynamics of a rank-one multiplicative perturbation of a unitary matrix
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 13
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.
corr_author: '1'
date_created: 2022-08-07T22:02:00Z
date_published: 2023-04-01T00:00:00Z
date_updated: 2024-10-09T21:03:02Z
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: '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.
corr_author: '1'
date_created: 2023-12-10T23:01:00Z
date_published: 2023-11-01T00:00:00Z
date_updated: 2025-09-09T13:41:08Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/22-AIHP1304
ec_funded: 1
external_id:
arxiv:
- '2112.11382'
isi:
- '001098456400010'
intvolume: ' 59'
isi: 1
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 59
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.
corr_author: '1'
date_created: 2023-02-26T23:01:01Z
date_published: 2023-02-08T00:00:00Z
date_updated: 2025-04-14T07:44:00Z
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.
corr_author: '1'
date_created: 2023-03-05T23:01:05Z
date_published: 2023-05-01T00:00:00Z
date_updated: 2025-04-14T07:57:19Z
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.
corr_author: '1'
date_created: 2023-03-26T22:01:08Z
date_published: 2023-02-01T00:00:00Z
date_updated: 2025-04-14T07:57:19Z
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.
corr_author: '1'
date_created: 2023-04-02T22:01:11Z
date_published: 2023-07-01T00:00:00Z
date_updated: 2025-04-14T07:57:19Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00220-023-04692-y
ec_funded: 1
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isi:
- '000957343500001'
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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
relation: main_file
success: 1
file_date_updated: 2023-10-04T12:09:18Z
has_accepted_license: '1'
intvolume: ' 401'
isi: 1
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'
...