---
_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).
corr_author: '1'
date_created: 2022-02-06T23:01:30Z
date_published: 2022-04-15T00:00:00Z
date_updated: 2024-10-09T21:01:33Z
day: '15'
ddc:
- '500'
department:
- _id: LaEr
doi: 10.1016/j.jfa.2022.109394
external_id:
arxiv:
- '2102.09975'
isi:
- '000781239100004'
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month: '04'
oa: 1
oa_version: Published Version
publication: Journal of Functional Analysis
publication_identifier:
eissn:
- 1096-0783
issn:
- 0022-1236
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publisher: Elsevier
quality_controlled: '1'
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title: Thermalisation for Wigner matrices
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legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
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user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 282
year: '2022'
...
---
_id: '11332'
abstract:
- lang: eng
text: We show that the fluctuations of the largest eigenvalue of a real symmetric
or complex Hermitian Wigner matrix of size N converge to the Tracy–Widom laws
at a rate O(N^{-1/3+\omega }), as N tends to infinity. For Wigner matrices this
improves the previous rate O(N^{-2/9+\omega }) obtained by Bourgade (J Eur Math
Soc, 2021) for generalized Wigner matrices. Our result follows from a Green function
comparison theorem, originally introduced by Erdős et al. (Adv Math 229(3):1435–1515,
2012) to prove edge universality, on a finer spectral parameter scale with improved
error estimates. The proof relies on the continuous Green function flow induced
by a matrix-valued Ornstein–Uhlenbeck process. Precise estimates on leading contributions
from the third and fourth order moments of the matrix entries are obtained using
iterative cumulant expansions and recursive comparisons for correlation functions,
along with uniform convergence estimates for correlation kernels of the Gaussian
invariant ensembles.
acknowledgement: Kevin Schnelli is supported in parts by the Swedish Research Council
Grant VR-2017-05195, and the Knut and Alice Wallenberg Foundation. Yuanyuan Xu is
supported by the Swedish Research Council Grant VR-2017-05195 and the ERC Advanced
Grant “RMTBeyond” No. 101020331.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Kevin
full_name: Schnelli, Kevin
id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
last_name: Schnelli
orcid: 0000-0003-0954-3231
- first_name: Yuanyuan
full_name: Xu, Yuanyuan
id: 7902bdb1-a2a4-11eb-a164-c9216f71aea3
last_name: Xu
orcid: 0000-0003-1559-1205
citation:
ama: Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest
Eigenvalue of Wigner matrices. Communications in Mathematical Physics.
2022;393:839-907. doi:10.1007/s00220-022-04377-y
apa: Schnelli, K., & Xu, Y. (2022). Convergence rate to the Tracy–Widom laws
for the largest Eigenvalue of Wigner matrices. Communications in Mathematical
Physics. Springer Nature. https://doi.org/10.1007/s00220-022-04377-y
chicago: Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom
Laws for the Largest Eigenvalue of Wigner Matrices.” Communications in Mathematical
Physics. Springer Nature, 2022. https://doi.org/10.1007/s00220-022-04377-y.
ieee: K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest
Eigenvalue of Wigner matrices,” Communications in Mathematical Physics,
vol. 393. Springer Nature, pp. 839–907, 2022.
ista: Schnelli K, Xu Y. 2022. Convergence rate to the Tracy–Widom laws for the largest
Eigenvalue of Wigner matrices. Communications in Mathematical Physics. 393, 839–907.
mla: Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws
for the Largest Eigenvalue of Wigner Matrices.” Communications in Mathematical
Physics, vol. 393, Springer Nature, 2022, pp. 839–907, doi:10.1007/s00220-022-04377-y.
short: K. Schnelli, Y. Xu, Communications in Mathematical Physics 393 (2022) 839–907.
date_created: 2022-04-24T22:01:44Z
date_published: 2022-07-01T00:00:00Z
date_updated: 2025-06-11T14:01:05Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00220-022-04377-y
ec_funded: 1
external_id:
arxiv:
- '2102.04330'
isi:
- '000782737200001'
pmid:
- '35765414'
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page: 839-907
pmid: 1
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- _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: Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner
matrices
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
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type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 393
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: '10623'
abstract:
- lang: eng
text: We investigate the BCS critical temperature Tc in the high-density limit and
derive an asymptotic formula, which strongly depends on the behavior of the interaction
potential V on the Fermi-surface. Our results include a rigorous confirmation
for the behavior of Tc at high densities proposed by Langmann et al. (Phys Rev
Lett 122:157001, 2019) and identify precise conditions under which superconducting
domes arise in BCS theory.
acknowledgement: I am very grateful to Robert Seiringer for his guidance during this
project and for many valuable comments on an earlier version of the manuscript.
Moreover, I would like to thank Asbjørn Bækgaard Lauritsen for many helpful discussions
and comments, pointing out the reference [22] and for his involvement in a closely
related joint project [13]. Finally, I am grateful to Christian Hainzl for valuable
comments on an earlier version of the manuscript and Andreas Deuchert for interesting
discussions.
article_number: '3'
article_processing_charge: Yes (via OA deal)
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
citation:
ama: Henheik SJ. The BCS critical temperature at high density. Mathematical Physics,
Analysis and Geometry. 2022;25(1). doi:10.1007/s11040-021-09415-0
apa: Henheik, S. J. (2022). The BCS critical temperature at high density. Mathematical
Physics, Analysis and Geometry. Springer Nature. https://doi.org/10.1007/s11040-021-09415-0
chicago: Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” Mathematical
Physics, Analysis and Geometry. Springer Nature, 2022. https://doi.org/10.1007/s11040-021-09415-0.
ieee: S. J. Henheik, “The BCS critical temperature at high density,” Mathematical
Physics, Analysis and Geometry, vol. 25, no. 1. Springer Nature, 2022.
ista: Henheik SJ. 2022. The BCS critical temperature at high density. Mathematical
Physics, Analysis and Geometry. 25(1), 3.
mla: Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” Mathematical
Physics, Analysis and Geometry, vol. 25, no. 1, 3, Springer Nature, 2022,
doi:10.1007/s11040-021-09415-0.
short: S.J. Henheik, Mathematical Physics, Analysis and Geometry 25 (2022).
corr_author: '1'
date_created: 2022-01-13T15:40:53Z
date_published: 2022-01-11T00:00:00Z
date_updated: 2026-04-07T12:37:10Z
day: '11'
ddc:
- '514'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1007/s11040-021-09415-0
ec_funded: 1
external_id:
arxiv:
- '2106.02015'
isi:
- '000741387600001'
file:
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checksum: d44f8123a52592a75b2c3b8ee2cd2435
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creator: cchlebak
date_created: 2022-01-14T07:27:45Z
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- geometry and topology
- mathematical physics
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- iso: eng
month: '01'
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call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Mathematical Physics, Analysis and Geometry
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- 1385-0172
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publisher: Springer Nature
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title: The BCS critical temperature at high density
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type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 25
year: '2022'
...
---
_id: '12184'
abstract:
- lang: eng
text: We review recent results on adiabatic theory for ground states of extended
gapped fermionic lattice systems under several different assumptions. More precisely,
we present generalized super-adiabatic theorems for extended but finite and infinite
systems, assuming either a uniform gap or a gap in the bulk above the unperturbed
ground state. The goal of this Review is to provide an overview of these adiabatic
theorems and briefly outline the main ideas and techniques required in their proofs.
acknowledgement: "It is a pleasure to thank Stefan Teufel for numerous interesting
discussions, fruitful collaboration, and many helpful comments on an earlier version
of the manuscript. J.H. acknowledges partial financial support from the ERC Advanced
Grant No. 101020331 “Random\r\nmatrices beyond Wigner-Dyson-Mehta.” T.W. acknowledges
financial support from the DFG research unit FOR 5413 “Long-range interacting quantum
spin systems out of equilibrium: Experiment, Theory and Mathematics.\" "
article_number: '121101'
article_processing_charge: No
article_type: original
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. On adiabatic theory for extended fermionic lattice systems.
Journal of Mathematical Physics. 2022;63(12). doi:10.1063/5.0123441
apa: Henheik, S. J., & Wessel, T. (2022). On adiabatic theory for extended fermionic
lattice systems. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0123441
chicago: Henheik, Sven Joscha, and Tom Wessel. “On Adiabatic Theory for Extended
Fermionic Lattice Systems.” Journal of Mathematical Physics. AIP Publishing,
2022. https://doi.org/10.1063/5.0123441.
ieee: S. J. Henheik and T. Wessel, “On adiabatic theory for extended fermionic lattice
systems,” Journal of Mathematical Physics, vol. 63, no. 12. AIP Publishing,
2022.
ista: Henheik SJ, Wessel T. 2022. On adiabatic theory for extended fermionic lattice
systems. Journal of Mathematical Physics. 63(12), 121101.
mla: Henheik, Sven Joscha, and Tom Wessel. “On Adiabatic Theory for Extended Fermionic
Lattice Systems.” Journal of Mathematical Physics, vol. 63, no. 12, 121101,
AIP Publishing, 2022, doi:10.1063/5.0123441.
short: S.J. Henheik, T. Wessel, Journal of Mathematical Physics 63 (2022).
corr_author: '1'
date_created: 2023-01-15T23:00:52Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2026-04-07T12:37:10Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1063/5.0123441
ec_funded: 1
external_id:
arxiv:
- '2208.12220'
isi:
- '000905776200001'
file:
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checksum: 213b93750080460718c050e4967cfdb4
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month: '12'
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grant_number: '101020331'
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title: On adiabatic theory for extended fermionic lattice systems
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type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 63
year: '2022'
...
---
_id: '10642'
abstract:
- lang: eng
text: Based on a result by Yarotsky (J Stat Phys 118, 2005), we prove that localized
but otherwise arbitrary perturbations of weakly interacting quantum spin systems
with uniformly gapped on-site terms change the ground state of such a system only
locally, even if they close the spectral gap. We call this a strong version of
the local perturbations perturb locally (LPPL) principle which is known to hold
for much more general gapped systems, but only for perturbations that do not close
the spectral gap of the Hamiltonian. We also extend this strong LPPL-principle
to Hamiltonians that have the appropriate structure of gapped on-site terms and
weak interactions only locally in some region of space. While our results are
technically corollaries to a theorem of Yarotsky, we expect that the paradigm
of systems with a locally gapped ground state that is completely insensitive to
the form of the Hamiltonian elsewhere extends to other situations and has important
physical consequences.
acknowledgement: J. H. acknowledges partial financial support by the ERC Advanced
Grant “RMTBeyond” No. 101020331. S. T. thanks Marius Lemm and Simone Warzel for
very helpful comments and discussions and Jürg Fröhlich for references to the literature.
Open Access funding enabled and organized by Projekt DEAL.
article_number: '9'
article_processing_charge: No
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: Stefan
full_name: Teufel, Stefan
last_name: Teufel
- first_name: Tom
full_name: Wessel, Tom
last_name: Wessel
citation:
ama: Henheik SJ, Teufel S, Wessel T. Local stability of ground states in locally
gapped and weakly interacting quantum spin systems. Letters in Mathematical
Physics. 2022;112(1). doi:10.1007/s11005-021-01494-y
apa: Henheik, S. J., Teufel, S., & Wessel, T. (2022). Local stability of ground
states in locally gapped and weakly interacting quantum spin systems. Letters
in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-021-01494-y
chicago: Henheik, Sven Joscha, Stefan Teufel, and Tom Wessel. “Local Stability of
Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.”
Letters in Mathematical Physics. Springer Nature, 2022. https://doi.org/10.1007/s11005-021-01494-y.
ieee: S. J. Henheik, S. Teufel, and T. Wessel, “Local stability of ground states
in locally gapped and weakly interacting quantum spin systems,” Letters in
Mathematical Physics, vol. 112, no. 1. Springer Nature, 2022.
ista: Henheik SJ, Teufel S, Wessel T. 2022. Local stability of ground states in
locally gapped and weakly interacting quantum spin systems. Letters in Mathematical
Physics. 112(1), 9.
mla: Henheik, Sven Joscha, et al. “Local Stability of Ground States in Locally Gapped
and Weakly Interacting Quantum Spin Systems.” Letters in Mathematical Physics,
vol. 112, no. 1, 9, Springer Nature, 2022, doi:10.1007/s11005-021-01494-y.
short: S.J. Henheik, S. Teufel, T. Wessel, Letters in Mathematical Physics 112 (2022).
date_created: 2022-01-18T16:18:25Z
date_published: 2022-01-18T00:00:00Z
date_updated: 2026-04-07T12:37:10Z
day: '18'
ddc:
- '530'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1007/s11005-021-01494-y
ec_funded: 1
external_id:
arxiv:
- '2106.13780'
isi:
- '000744930400001'
pmid:
- '35125630'
file:
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checksum: 7e8e69b76e892c305071a4736131fe18
content_type: application/pdf
creator: cchlebak
date_created: 2022-01-19T09:41:14Z
date_updated: 2022-01-19T09:41:14Z
file_id: '10647'
file_name: 2022_LettersMathPhys_Henheik.pdf
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- statistical and nonlinear physics
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
pmid: 1
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call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Letters in Mathematical Physics
publication_identifier:
eissn:
- 1573-0530
issn:
- 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '19540'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Local stability of ground states in locally gapped and weakly interacting quantum
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: 112
year: '2022'
...
---
_id: '11732'
abstract:
- lang: eng
text: We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic
formula, which strongly depends on the strength of the interaction potential V
on the Fermi surface. In combination with the recent result by one of us (Math.
Phys. Anal. Geom. 25, 3, 2022) on the critical temperature Tc at high densities,
we prove the universality of the ratio of the energy gap and the critical temperature.
acknowledgement: "We are grateful to Robert Seiringer for helpful discussions and
many valuable comments\r\non an earlier version of the manuscript. J.H. acknowledges
partial financial support by the ERC Advanced Grant “RMTBeyond’ No. 101020331. Open
access funding provided by Institute of Science and Technology (IST Austria)"
article_number: '5'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- first_name: Asbjørn Bækgaard
full_name: Lauritsen, Asbjørn Bækgaard
id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1
last_name: Lauritsen
orcid: 0000-0003-4476-2288
citation:
ama: Henheik SJ, Lauritsen AB. The BCS energy gap at high density. Journal of
Statistical Physics. 2022;189. doi:10.1007/s10955-022-02965-9
apa: Henheik, S. J., & Lauritsen, A. B. (2022). The BCS energy gap at high density.
Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02965-9
chicago: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap
at High Density.” Journal of Statistical Physics. Springer Nature, 2022.
https://doi.org/10.1007/s10955-022-02965-9.
ieee: S. J. Henheik and A. B. Lauritsen, “The BCS energy gap at high density,” Journal
of Statistical Physics, vol. 189. Springer Nature, 2022.
ista: Henheik SJ, Lauritsen AB. 2022. The BCS energy gap at high density. Journal
of Statistical Physics. 189, 5.
mla: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at
High Density.” Journal of Statistical Physics, vol. 189, 5, Springer Nature,
2022, doi:10.1007/s10955-022-02965-9.
short: S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022).
corr_author: '1'
date_created: 2022-08-05T11:36:56Z
date_published: 2022-07-29T00:00:00Z
date_updated: 2026-04-07T13:01:40Z
day: '29'
ddc:
- '530'
department:
- _id: GradSch
- _id: LaEr
- _id: RoSe
doi: 10.1007/s10955-022-02965-9
ec_funded: 1
external_id:
isi:
- '000833007200002'
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checksum: b398c4dbf65f71d417981d6e366427e9
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creator: dernst
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date_updated: 2022-08-08T07:36:34Z
file_id: '11746'
file_name: 2022_JourStatisticalPhysics_Henheik.pdf
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file_date_updated: 2022-08-08T07:36:34Z
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intvolume: ' 189'
isi: 1
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Journal of Statistical Physics
publication_identifier:
eissn:
- 1572-9613
issn:
- 0022-4715
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '19540'
relation: dissertation_contains
status: public
- id: '18135'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: The BCS energy gap at high density
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 189
year: '2022'
...
---
_id: '11135'
abstract:
- lang: eng
text: We consider a correlated NxN Hermitian random matrix with a polynomially decaying
metric correlation structure. By calculating the trace of the moments of the matrix
and using the summable decay of the cumulants, we show that its operator norm
is stochastically dominated by one.
article_number: '2250036'
article_processing_charge: No
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. On the operator norm of a Hermitian random matrix with correlated
entries. Random Matrices: Theory and Applications. 2022;11(4). doi:10.1142/s2010326322500368'
apa: 'Reker, J. (2022). On the operator norm of a Hermitian random matrix with correlated
entries. Random Matrices: Theory and Applications. World Scientific Publishing.
https://doi.org/10.1142/s2010326322500368'
chicago: 'Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated
Entries.” Random Matrices: Theory and Applications. World Scientific Publishing,
2022. https://doi.org/10.1142/s2010326322500368.'
ieee: 'J. Reker, “On the operator norm of a Hermitian random matrix with correlated
entries,” Random Matrices: Theory and Applications, vol. 11, no. 4. World
Scientific Publishing, 2022.'
ista: 'Reker J. 2022. On the operator norm of a Hermitian random matrix with correlated
entries. Random Matrices: Theory and Applications. 11(4), 2250036.'
mla: 'Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated
Entries.” Random Matrices: Theory and Applications, vol. 11, no. 4, 2250036,
World Scientific Publishing, 2022, doi:10.1142/s2010326322500368.'
short: 'J. Reker, Random Matrices: Theory and Applications 11 (2022).'
corr_author: '1'
date_created: 2022-04-08T07:11:12Z
date_published: 2022-10-01T00:00:00Z
date_updated: 2026-04-07T13:02:12Z
day: '01'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1142/s2010326322500368
external_id:
arxiv:
- '2103.03906'
isi:
- '000848873800001'
intvolume: ' 11'
isi: 1
issue: '4'
keyword:
- Discrete Mathematics and Combinatorics
- Statistics
- Probability and Uncertainty
- Statistics and Probability
- Algebra and Number Theory
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2103.03906'
month: '10'
oa: 1
oa_version: Preprint
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
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scopus_import: '1'
status: public
title: On the operator norm of a Hermitian random matrix with correlated entries
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 11
year: '2022'
...
---
_id: '15013'
abstract:
- lang: eng
text: We consider random n×n matrices X with independent and centered entries and
a general variance profile. We show that the spectral radius of X converges with
very high probability to the square root of the spectral radius of the variance
matrix of X when n tends to infinity. We also establish the optimal rate of convergence,
that is a new result even for general i.i.d. matrices beyond the explicitly solvable
Gaussian cases. The main ingredient is the proof of the local inhomogeneous circular
law [arXiv:1612.07776] at the spectral edge.
acknowledgement: Partially supported by ERC Starting Grant RandMat No. 715539 and
the SwissMap grant of Swiss National Science Foundation. Partially supported by
ERC Advanced Grant RanMat No. 338804. Partially supported by the Hausdorff Center
for Mathematics in Bonn.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Johannes
full_name: Alt, Johannes
id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
last_name: Alt
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
citation:
ama: Alt J, Erdös L, Krüger TH. Spectral radius of random matrices with independent
entries. Probability and Mathematical Physics. 2021;2(2):221-280. doi:10.2140/pmp.2021.2.221
apa: Alt, J., Erdös, L., & Krüger, T. H. (2021). Spectral radius of random matrices
with independent entries. Probability and Mathematical Physics. Mathematical
Sciences Publishers. https://doi.org/10.2140/pmp.2021.2.221
chicago: Alt, Johannes, László Erdös, and Torben H Krüger. “Spectral Radius of Random
Matrices with Independent Entries.” Probability and Mathematical Physics.
Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/pmp.2021.2.221.
ieee: J. Alt, L. Erdös, and T. H. Krüger, “Spectral radius of random matrices with
independent entries,” Probability and Mathematical Physics, vol. 2, no.
2. Mathematical Sciences Publishers, pp. 221–280, 2021.
ista: Alt J, Erdös L, Krüger TH. 2021. Spectral radius of random matrices with independent
entries. Probability and Mathematical Physics. 2(2), 221–280.
mla: Alt, Johannes, et al. “Spectral Radius of Random Matrices with Independent
Entries.” Probability and Mathematical Physics, vol. 2, no. 2, Mathematical
Sciences Publishers, 2021, pp. 221–80, doi:10.2140/pmp.2021.2.221.
short: J. Alt, L. Erdös, T.H. Krüger, Probability and Mathematical Physics 2 (2021)
221–280.
corr_author: '1'
date_created: 2024-02-18T23:01:03Z
date_published: 2021-05-21T00:00:00Z
date_updated: 2025-04-15T08:05:02Z
day: '21'
department:
- _id: LaEr
doi: 10.2140/pmp.2021.2.221
ec_funded: 1
external_id:
arxiv:
- '1907.13631'
intvolume: ' 2'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1907.13631
month: '05'
oa: 1
oa_version: Preprint
page: 221-280
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Probability and Mathematical Physics
publication_identifier:
eissn:
- 2690-1005
issn:
- 2690-0998
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Spectral radius of random matrices with independent entries
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2
year: '2021'
...
---
_id: '15259'
abstract:
- lang: eng
text: "We consider words Gi1⋯Gim involving i.i.d. complex Ginibre matrices and study
tracial expressions of their eigenvalues and singular values. We show that the
limit distribution of the squared singular values of every word of length m is
a Fuss–Catalan distribution with parameter \r\nm+1. This generalizes previous
results concerning powers of a complex Ginibre matrix and products of independent
Ginibre matrices. In addition, we find other combinatorial parameters of the word
that determine the second-order limits of the spectral statistics. For instance,
the so-called coperiod of a word characterizes the fluctuations of the eigenvalues.
We extend these results to words of general non-Hermitian matrices with i.i.d.
entries under moment-matching assumptions, band matrices, and sparse matrices.\r\nThese
results rely on the moments method and genus expansion, relating Gaussian matrix
integrals to the counting of compact orientable surfaces of a given genus. This
allows us to derive a central limit theorem for the trace of any word of complex
Ginibre matrices and their conjugate transposes, where all parameters are defined
topologically."
acknowledgement: "The authors would like to thank Gernot Akemann, Benson Au, Paul
Bourgade, Jesper Ipsen, Camille Male, Jamie Mingo, Doron Puder, Emily Redelmeier,
Roland Speicher, Wojciech Tarnowski and Ofer Zeitouni for useful discussions, comments
and references as well as the anonymous referee for a suggestion that greatly improved
one of the theorems.\r\nG.D. gratefully acknowledges support from the grants NSF
DMS-1812114 of P. Bourgade (PI) and NSF CAREER DMS-1653602 of L.-P. Arguin (PI),
as well as the European Union’s Horizon 2020 research and innovation programme under
the Marie Skłodowska-Curie Grant Agreement No. 754411."
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: Yuval
full_name: Peled, Yuval
last_name: Peled
citation:
ama: Dubach G, Peled Y. On words of non-Hermitian random matrices. The Annals
of Probability. 2021;49(4):1886-1916. doi:10.1214/20-aop1496
apa: Dubach, G., & Peled, Y. (2021). On words of non-Hermitian random matrices.
The Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/20-aop1496
chicago: Dubach, Guillaume, and Yuval Peled. “On Words of Non-Hermitian Random Matrices.”
The Annals of Probability. Institute of Mathematical Statistics, 2021.
https://doi.org/10.1214/20-aop1496.
ieee: G. Dubach and Y. Peled, “On words of non-Hermitian random matrices,” The
Annals of Probability, vol. 49, no. 4. Institute of Mathematical Statistics,
pp. 1886–1916, 2021.
ista: Dubach G, Peled Y. 2021. On words of non-Hermitian random matrices. The Annals
of Probability. 49(4), 1886–1916.
mla: Dubach, Guillaume, and Yuval Peled. “On Words of Non-Hermitian Random Matrices.”
The Annals of Probability, vol. 49, no. 4, Institute of Mathematical Statistics,
2021, pp. 1886–916, doi:10.1214/20-aop1496.
short: G. Dubach, Y. Peled, The Annals of Probability 49 (2021) 1886–1916.
corr_author: '1'
date_created: 2024-04-03T07:19:42Z
date_published: 2021-07-01T00:00:00Z
date_updated: 2025-09-10T10:13:20Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/20-aop1496
ec_funded: 1
external_id:
arxiv:
- '1904.04312'
isi:
- '000681349000008'
intvolume: ' 49'
isi: 1
issue: '4'
keyword:
- Statistics
- Probability and Uncertainty
- Statistics and Probability
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1904.04312
month: '07'
oa: 1
oa_version: Preprint
page: 1886-1916
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: The Annals of Probability
publication_identifier:
issn:
- 0091-1798
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: On words of non-Hermitian random matrices
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 49
year: '2021'
...
---
_id: '10221'
abstract:
- lang: eng
text: We prove that any deterministic matrix is approximately the identity in the
eigenbasis of a large random Wigner matrix with very high probability and with
an optimal error inversely proportional to the square root of the dimension. Our
theorem thus rigorously verifies the Eigenstate Thermalisation Hypothesis by Deutsch
(Phys Rev A 43:2046–2049, 1991) for the simplest chaotic quantum system, the Wigner
ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity
(QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing
previous probabilistic QUE results in Bourgade and Yau (Commun Math Phys 350:231–278,
2017) and Bourgade et al. (Commun Pure Appl Math 73:1526–1596, 2020).
acknowledgement: Open 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. Eigenstate thermalization hypothesis for
Wigner matrices. Communications in Mathematical Physics. 2021;388(2):1005–1048.
doi:10.1007/s00220-021-04239-z
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Eigenstate thermalization
hypothesis for Wigner matrices. Communications in Mathematical Physics.
Springer Nature. https://doi.org/10.1007/s00220-021-04239-z
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Eigenstate Thermalization
Hypothesis for Wigner Matrices.” Communications in Mathematical Physics.
Springer Nature, 2021. https://doi.org/10.1007/s00220-021-04239-z.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Eigenstate thermalization hypothesis
for Wigner matrices,” Communications in Mathematical Physics, vol. 388,
no. 2. Springer Nature, pp. 1005–1048, 2021.
ista: Cipolloni G, Erdös L, Schröder DJ. 2021. Eigenstate thermalization hypothesis
for Wigner matrices. Communications in Mathematical Physics. 388(2), 1005–1048.
mla: Cipolloni, Giorgio, et al. “Eigenstate Thermalization Hypothesis for Wigner
Matrices.” Communications in Mathematical Physics, vol. 388, no. 2, Springer
Nature, 2021, pp. 1005–1048, doi:10.1007/s00220-021-04239-z.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics
388 (2021) 1005–1048.
corr_author: '1'
date_created: 2021-11-07T23:01:25Z
date_published: 2021-10-29T00:00:00Z
date_updated: 2025-04-15T06:53:08Z
day: '29'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00220-021-04239-z
external_id:
arxiv:
- '2012.13215'
isi:
- '000712232700001'
file:
- access_level: open_access
checksum: a2c7b6f5d23b5453cd70d1261272283b
content_type: application/pdf
creator: cchlebak
date_created: 2022-02-02T10:19:55Z
date_updated: 2022-02-02T10:19:55Z
file_id: '10715'
file_name: 2021_CommunMathPhys_Cipolloni.pdf
file_size: 841426
relation: main_file
success: 1
file_date_updated: 2022-02-02T10:19:55Z
has_accepted_license: '1'
intvolume: ' 388'
isi: 1
issue: '2'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 1005–1048
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
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: Eigenstate thermalization hypothesis 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: 388
year: '2021'
...
---
_id: '10285'
abstract:
- lang: eng
text: We study the overlaps between right and left eigenvectors for random matrices
of the spherical ensemble, as well as truncated unitary ensembles in the regime
where half of the matrix at least is truncated. These two integrable models exhibit
a form of duality, and the essential steps of our investigation can therefore
be performed in parallel. In every case, conditionally on all eigenvalues, diagonal
overlaps are shown to be distributed as a product of independent random variables
with explicit distributions. This enables us to prove that the scaled diagonal
overlaps, conditionally on one eigenvalue, converge in distribution to a heavy-tail
limit, namely, the inverse of a γ2 distribution. We also provide formulae for
the conditional expectation of diagonal and off-diagonal overlaps, either with
respect to one eigenvalue, or with respect to the whole spectrum. These results,
analogous to what is known for the complex Ginibre ensemble, can be obtained in
these cases thanks to integration techniques inspired from a previous work by
Forrester & Krishnapur.
acknowledgement: We acknowledge partial support from the grants NSF DMS-1812114 of
P. Bourgade (PI) and NSF CAREER DMS-1653602 of L.-P. Arguin (PI). This project has
also received funding from the European Union’s Horizon 2020 research and innovation
programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. We would
like to thank Paul Bourgade and László Erdős for many helpful comments.
article_number: '124'
article_processing_charge: No
article_type: original
author:
- first_name: Guillaume
full_name: Dubach, Guillaume
id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E
last_name: Dubach
orcid: 0000-0001-6892-8137
citation:
ama: Dubach G. On eigenvector statistics in the spherical and truncated unitary
ensembles. Electronic Journal of Probability. 2021;26. doi:10.1214/21-EJP686
apa: Dubach, G. (2021). On eigenvector statistics in the spherical and truncated
unitary ensembles. Electronic Journal of Probability. Institute of Mathematical
Statistics. https://doi.org/10.1214/21-EJP686
chicago: Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated
Unitary Ensembles.” Electronic Journal of Probability. Institute of Mathematical
Statistics, 2021. https://doi.org/10.1214/21-EJP686.
ieee: G. Dubach, “On eigenvector statistics in the spherical and truncated unitary
ensembles,” Electronic Journal of Probability, vol. 26. Institute of Mathematical
Statistics, 2021.
ista: Dubach G. 2021. On eigenvector statistics in the spherical and truncated unitary
ensembles. Electronic Journal of Probability. 26, 124.
mla: Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated
Unitary Ensembles.” Electronic Journal of Probability, vol. 26, 124, Institute
of Mathematical Statistics, 2021, doi:10.1214/21-EJP686.
short: G. Dubach, Electronic Journal of Probability 26 (2021).
date_created: 2021-11-14T23:01:25Z
date_published: 2021-09-28T00:00:00Z
date_updated: 2025-04-14T07:43:47Z
day: '28'
ddc:
- '519'
department:
- _id: LaEr
doi: 10.1214/21-EJP686
ec_funded: 1
file:
- access_level: open_access
checksum: 1c975afb31460277ce4d22b93538e5f9
content_type: application/pdf
creator: cchlebak
date_created: 2021-11-15T10:10:17Z
date_updated: 2021-11-15T10:10:17Z
file_id: '10288'
file_name: 2021_ElecJournalProb_Dubach.pdf
file_size: 735940
relation: main_file
success: 1
file_date_updated: 2021-11-15T10:10:17Z
has_accepted_license: '1'
intvolume: ' 26'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Electronic Journal of Probability
publication_identifier:
eissn:
- 1083-6489
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: On eigenvector statistics in the spherical and truncated unitary ensembles
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 26
year: '2021'
...
---
_id: '8373'
abstract:
- lang: eng
text: It is well known that special Kubo-Ando operator means admit divergence center
interpretations, moreover, they are also mean squared error estimators for certain
metrics on positive definite operators. In this paper we give a divergence center
interpretation for every symmetric Kubo-Ando mean. This characterization of the
symmetric means naturally leads to a definition of weighted and multivariate versions
of a large class of symmetric Kubo-Ando means. We study elementary properties
of these weighted multivariate means, and note in particular that in the special
case of the geometric mean we recover the weighted A#H-mean introduced by Kim,
Lawson, and Lim.
acknowledgement: "The authors are grateful to Milán Mosonyi for fruitful discussions
on the topic, and to the anonymous referee for his/her comments and suggestions.\r\nJ.
Pitrik was supported by the Hungarian Academy of Sciences Lendület-Momentum Grant
for Quantum Information Theory, No. 96 141, and by Hungarian National Research,
Development and Innovation Office (NKFIH) via grants no. K119442, no. K124152, and
no. KH129601. D. Virosztek was supported by the ISTFELLOW program of the Institute
of Science and Technology Austria (project code IC1027FELL01), by the European Union's
Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant
Agreement No. 846294, and partially supported by the Hungarian National Research,
Development and Innovation Office (NKFIH) via grants no. K124152, and no. KH129601."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: József
full_name: Pitrik, József
last_name: Pitrik
- first_name: Daniel
full_name: Virosztek, Daniel
id: 48DB45DA-F248-11E8-B48F-1D18A9856A87
last_name: Virosztek
orcid: 0000-0003-1109-5511
citation:
ama: Pitrik J, Virosztek D. A divergence center interpretation of general symmetric
Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra
and its Applications. 2021;609:203-217. doi:10.1016/j.laa.2020.09.007
apa: Pitrik, J., & Virosztek, D. (2021). A divergence center interpretation
of general symmetric Kubo-Ando means, and related weighted multivariate operator
means. Linear Algebra and Its Applications. Elsevier. https://doi.org/10.1016/j.laa.2020.09.007
chicago: Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation
of General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator
Means.” Linear Algebra and Its Applications. Elsevier, 2021. https://doi.org/10.1016/j.laa.2020.09.007.
ieee: J. Pitrik and D. Virosztek, “A divergence center interpretation of general
symmetric Kubo-Ando means, and related weighted multivariate operator means,”
Linear Algebra and its Applications, vol. 609. Elsevier, pp. 203–217, 2021.
ista: Pitrik J, Virosztek D. 2021. A divergence center interpretation of general
symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear
Algebra and its Applications. 609, 203–217.
mla: Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation of
General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator
Means.” Linear Algebra and Its Applications, vol. 609, Elsevier, 2021,
pp. 203–17, doi:10.1016/j.laa.2020.09.007.
short: J. Pitrik, D. Virosztek, Linear Algebra and Its Applications 609 (2021) 203–217.
date_created: 2020-09-11T08:35:50Z
date_published: 2021-01-15T00:00:00Z
date_updated: 2025-04-14T07:50:40Z
day: '15'
department:
- _id: LaEr
doi: 10.1016/j.laa.2020.09.007
ec_funded: 1
external_id:
arxiv:
- '2002.11678'
isi:
- '000581730500011'
intvolume: ' 609'
isi: 1
keyword:
- Kubo-Ando mean
- weighted multivariate mean
- barycenter
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2002.11678
month: '01'
oa: 1
oa_version: Preprint
page: 203-217
project:
- _id: 26A455A6-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '846294'
name: Geometric study of Wasserstein spaces and free probability
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Linear Algebra and its Applications
publication_identifier:
issn:
- 0024-3795
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: A divergence center interpretation of general symmetric Kubo-Ando means, and
related weighted multivariate operator means
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 609
year: '2021'
...
---
_id: '9036'
abstract:
- lang: eng
text: In this short note, we prove that the square root of the quantum Jensen-Shannon
divergence is a true metric on the cone of positive matrices, and hence in particular
on the quantum state space.
acknowledgement: D. Virosztek was supported by the European Union's Horizon 2020 research
and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 846294,
and partially supported by the Hungarian National Research, Development and Innovation
Office (NKFIH) via grants no. K124152, and no. KH129601.
article_number: '107595'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Daniel
full_name: Virosztek, Daniel
id: 48DB45DA-F248-11E8-B48F-1D18A9856A87
last_name: Virosztek
orcid: 0000-0003-1109-5511
citation:
ama: Virosztek D. The metric property of the quantum Jensen-Shannon divergence.
Advances in Mathematics. 2021;380(3). doi:10.1016/j.aim.2021.107595
apa: Virosztek, D. (2021). The metric property of the quantum Jensen-Shannon divergence.
Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2021.107595
chicago: Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.”
Advances in Mathematics. Elsevier, 2021. https://doi.org/10.1016/j.aim.2021.107595.
ieee: D. Virosztek, “The metric property of the quantum Jensen-Shannon divergence,”
Advances in Mathematics, vol. 380, no. 3. Elsevier, 2021.
ista: Virosztek D. 2021. The metric property of the quantum Jensen-Shannon divergence.
Advances in Mathematics. 380(3), 107595.
mla: Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.”
Advances in Mathematics, vol. 380, no. 3, 107595, Elsevier, 2021, doi:10.1016/j.aim.2021.107595.
short: D. Virosztek, Advances in Mathematics 380 (2021).
date_created: 2021-01-22T17:55:17Z
date_published: 2021-03-26T00:00:00Z
date_updated: 2025-04-14T07:50:40Z
day: '26'
department:
- _id: LaEr
doi: 10.1016/j.aim.2021.107595
ec_funded: 1
external_id:
arxiv:
- '1910.10447'
isi:
- '000619676100035'
intvolume: ' 380'
isi: 1
issue: '3'
keyword:
- General Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1910.10447
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: 26A455A6-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '846294'
name: Geometric study of Wasserstein spaces and free probability
publication: Advances in Mathematics
publication_identifier:
issn:
- 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: The metric property of the quantum Jensen-Shannon divergence
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 380
year: '2021'
...
---
_id: '9230'
abstract:
- lang: eng
text: "We consider a model of the Riemann zeta function on the critical axis and
study its maximum over intervals of length (log T)θ, where θ is either fixed or
tends to zero at a suitable rate.\r\nIt is shown that the deterministic level
of the maximum interpolates smoothly between the ones\r\nof log-correlated variables
and of i.i.d. random variables, exhibiting a smooth transition ‘from\r\n3/4 to
1/4’ in the second order. This provides a natural context where extreme value
statistics of\r\nlog-correlated variables with time-dependent variance and rate
occur. A key ingredient of the\r\nproof is a precise upper tail tightness estimate
for the maximum of the model on intervals of\r\nsize one, that includes a Gaussian
correction. This correction is expected to be present for the\r\nRiemann zeta
function and pertains to the question of the correct order of the maximum of\r\nthe
zeta function in large intervals."
acknowledgement: The research of L.-P. A. is supported in part by the grant NSF CAREER
DMS-1653602. G. D. gratefully acknowledges support from the European Union’s Horizon
2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement
No. 754411. The research of L. H. is supported in part by the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation) through Project-ID 233630050 -TRR 146, Project-ID
443891315 within SPP 2265 and Project-ID 446173099.
article_number: '2103.04817'
article_processing_charge: No
arxiv: 1
author:
- first_name: Louis-Pierre
full_name: Arguin, Louis-Pierre
last_name: Arguin
- first_name: Guillaume
full_name: Dubach, Guillaume
id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E
last_name: Dubach
orcid: 0000-0001-6892-8137
- first_name: Lisa
full_name: Hartung, Lisa
last_name: Hartung
citation:
ama: Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta
function over intervals of varying length. arXiv. doi:10.48550/arXiv.2103.04817
apa: Arguin, L.-P., Dubach, G., & Hartung, L. (n.d.). Maxima of a random model
of the Riemann zeta function over intervals of varying length. arXiv. https://doi.org/10.48550/arXiv.2103.04817
chicago: Arguin, Louis-Pierre, Guillaume Dubach, and Lisa Hartung. “Maxima of a
Random Model of the Riemann Zeta Function over Intervals of Varying Length.” ArXiv,
n.d. https://doi.org/10.48550/arXiv.2103.04817.
ieee: L.-P. Arguin, G. Dubach, and L. Hartung, “Maxima of a random model of the
Riemann zeta function over intervals of varying length,” arXiv. .
ista: Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta
function over intervals of varying length. arXiv, 2103.04817.
mla: Arguin, Louis-Pierre, et al. “Maxima of a Random Model of the Riemann Zeta
Function over Intervals of Varying Length.” ArXiv, 2103.04817, doi:10.48550/arXiv.2103.04817.
short: L.-P. Arguin, G. Dubach, L. Hartung, ArXiv (n.d.).
date_created: 2021-03-09T11:08:15Z
date_published: 2021-03-08T00:00:00Z
date_updated: 2025-04-14T07:43:51Z
day: '08'
department:
- _id: LaEr
doi: 10.48550/arXiv.2103.04817
ec_funded: 1
external_id:
arxiv:
- '2103.04817'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2103.04817
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: arXiv
publication_status: submitted
status: public
title: Maxima of a random model of the Riemann zeta function over intervals of varying
length
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '9281'
abstract:
- lang: eng
text: We comment on two formal proofs of Fermat's sum of two squares theorem, written
using the Mathematical Components libraries of the Coq proof assistant. The first
one follows Zagier's celebrated one-sentence proof; the second follows David Christopher's
recent new proof relying on partition-theoretic arguments. Both formal proofs
rely on a general property of involutions of finite sets, of independent interest.
The proof technique consists for the most part of automating recurrent tasks (such
as case distinctions and computations on natural numbers) via ad hoc tactics.
article_number: '2103.11389'
article_processing_charge: No
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: Fabian
full_name: Mühlböck, Fabian
id: 6395C5F6-89DF-11E9-9C97-6BDFE5697425
last_name: Mühlböck
orcid: 0000-0003-1548-0177
citation:
ama: Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. arXiv.
doi:10.48550/arXiv.2103.11389
apa: Dubach, G., & Mühlböck, F. (n.d.). Formal verification of Zagier’s one-sentence
proof. arXiv. https://doi.org/10.48550/arXiv.2103.11389
chicago: Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s
One-Sentence Proof.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2103.11389.
ieee: G. Dubach and F. Mühlböck, “Formal verification of Zagier’s one-sentence proof,”
arXiv. .
ista: Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof.
arXiv, 2103.11389.
mla: Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence
Proof.” ArXiv, 2103.11389, doi:10.48550/arXiv.2103.11389.
short: G. Dubach, F. Mühlböck, ArXiv (n.d.).
corr_author: '1'
date_created: 2021-03-23T05:38:48Z
date_published: 2021-03-21T00:00:00Z
date_updated: 2025-04-15T06:26:12Z
day: '21'
department:
- _id: LaEr
- _id: ToHe
doi: 10.48550/arXiv.2103.11389
ec_funded: 1
external_id:
arxiv:
- '2103.11389'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2103.11389
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: arXiv
publication_status: submitted
related_material:
record:
- id: '9946'
relation: other
status: public
status: public
title: Formal verification of Zagier's one-sentence proof
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '9912'
abstract:
- lang: eng
text: "In the customary random matrix model for transport in quantum dots with M
internal degrees of freedom coupled to a chaotic environment via \U0001D441≪\U0001D440
channels, the density \U0001D70C of transmission eigenvalues is computed from
a specific invariant ensemble for which explicit formula for the joint probability
density of all eigenvalues is available. We revisit this problem in the large
N regime allowing for (i) arbitrary ratio \U0001D719:=\U0001D441/\U0001D440≤1;
and (ii) general distributions for the matrix elements of the Hamiltonian of the
quantum dot. In the limit \U0001D719→0, we recover the formula for the density
\U0001D70C that Beenakker (Rev Mod Phys 69:731–808, 1997) has derived for a special
matrix ensemble. We also prove that the inverse square root singularity of the
density at zero and full transmission in Beenakker’s formula persists for any
\U0001D719<1 but in the borderline case \U0001D719=1 an anomalous \U0001D706−2/3
singularity arises at zero. To access this level of generality, we develop the
theory of global and local laws on the spectral density of a large class of noncommutative
rational expressions in large random matrices with i.i.d. entries."
acknowledgement: The authors are very grateful to Yan Fyodorov for discussions on
the physical background and for providing references, and to the anonymous referee
for numerous valuable remarks.
article_processing_charge: Yes (in subscription journal)
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: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: Yuriy
full_name: Nemish, Yuriy
id: 4D902E6A-F248-11E8-B48F-1D18A9856A87
last_name: Nemish
orcid: 0000-0002-7327-856X
citation:
ama: Erdös L, Krüger TH, Nemish Y. Scattering in quantum dots via noncommutative
rational functions. Annales Henri Poincaré . 2021;22:4205–4269. doi:10.1007/s00023-021-01085-6
apa: Erdös, L., Krüger, T. H., & Nemish, Y. (2021). Scattering in quantum dots
via noncommutative rational functions. Annales Henri Poincaré . Springer
Nature. https://doi.org/10.1007/s00023-021-01085-6
chicago: Erdös, László, Torben H Krüger, and Yuriy Nemish. “Scattering in Quantum
Dots via Noncommutative Rational Functions.” Annales Henri Poincaré . Springer
Nature, 2021. https://doi.org/10.1007/s00023-021-01085-6.
ieee: L. Erdös, T. H. Krüger, and Y. Nemish, “Scattering in quantum dots via noncommutative
rational functions,” Annales Henri Poincaré , vol. 22. Springer Nature,
pp. 4205–4269, 2021.
ista: Erdös L, Krüger TH, Nemish Y. 2021. Scattering in quantum dots via noncommutative
rational functions. Annales Henri Poincaré . 22, 4205–4269.
mla: Erdös, László, et al. “Scattering in Quantum Dots via Noncommutative Rational
Functions.” Annales Henri Poincaré , vol. 22, Springer Nature, 2021, pp.
4205–4269, doi:10.1007/s00023-021-01085-6.
short: L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré 22 (2021) 4205–4269.
date_created: 2021-08-15T22:01:29Z
date_published: 2021-12-01T00:00:00Z
date_updated: 2025-04-15T08:04:59Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00023-021-01085-6
ec_funded: 1
external_id:
arxiv:
- '1911.05112'
isi:
- '000681531500001'
file:
- access_level: open_access
checksum: 8d6bac0e2b0a28539608b0538a8e3b38
content_type: application/pdf
creator: dernst
date_created: 2022-05-12T12:50:27Z
date_updated: 2022-05-12T12:50:27Z
file_id: '11365'
file_name: 2021_AnnHenriPoincare_Erdoes.pdf
file_size: 1162454
relation: main_file
success: 1
file_date_updated: 2022-05-12T12:50:27Z
has_accepted_license: '1'
intvolume: ' 22'
isi: 1
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 4205–4269
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: 'Annales Henri Poincaré '
publication_identifier:
eissn:
- 1424-0661
issn:
- 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Scattering in quantum dots via noncommutative rational functions
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: 22
year: '2021'
...
---
_id: '9412'
abstract:
- lang: eng
text: We extend our recent result [22] on the central limit theorem for the linear
eigenvalue statistics of non-Hermitian matrices X with independent, identically
distributed complex entries to the real symmetry class. We find that the expectation
and variance substantially differ from their complex counterparts, reflecting
(i) the special spectral symmetry of real matrices onto the real axis; and (ii)
the fact that real i.i.d. matrices have many real eigenvalues. Our result generalizes
the previously known special cases where either the test function is analytic
[49] or the first four moments of the matrix elements match the real Gaussian
[59, 44]. The key element of the proof is the analysis of several weakly dependent
Dyson Brownian motions (DBMs). The conceptual novelty of the real case compared
with [22] is that the correlation structure of the stochastic differentials in
each individual DBM is non-trivial, potentially even jeopardising its well-posedness.
article_number: '24'
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: 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. Fluctuation around the circular law for
random matrices with real entries. Electronic Journal of Probability. 2021;26.
doi:10.1214/21-EJP591
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Fluctuation around
the circular law for random matrices with real entries. Electronic Journal
of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-EJP591
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Fluctuation
around the Circular Law for Random Matrices with Real Entries.” Electronic
Journal of Probability. Institute of Mathematical Statistics, 2021. https://doi.org/10.1214/21-EJP591.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Fluctuation around the circular
law for random matrices with real entries,” Electronic Journal of Probability,
vol. 26. Institute of Mathematical Statistics, 2021.
ista: Cipolloni G, Erdös L, Schröder DJ. 2021. Fluctuation around the circular law
for random matrices with real entries. Electronic Journal of Probability. 26,
24.
mla: Cipolloni, Giorgio, et al. “Fluctuation around the Circular Law for Random
Matrices with Real Entries.” Electronic Journal of Probability, vol. 26,
24, Institute of Mathematical Statistics, 2021, doi:10.1214/21-EJP591.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability
26 (2021).
date_created: 2021-05-23T22:01:44Z
date_published: 2021-03-23T00:00:00Z
date_updated: 2026-04-02T14:00:37Z
day: '23'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1214/21-EJP591
ec_funded: 1
external_id:
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- '2002.02438'
isi:
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title: Fluctuation around the circular law for random matrices with real entries
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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)
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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).
corr_author: '1'
date_created: 2020-10-04T22:01:37Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2026-04-02T14:03:52Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00440-020-01003-7
ec_funded: 1
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- '1908.00969'
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call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
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call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- 1432-2064
issn:
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publication_status: published
publisher: Springer Nature
quality_controlled: '1'
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title: Edge universality for non-Hermitian random matrices
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---
_id: '9550'
abstract:
- lang: eng
text: 'We prove that the energy of any eigenvector of a sum of several independent
large Wigner matrices is equally distributed among these matrices with very high
precision. This shows a particularly strong microcanonical form of the equipartition
principle for quantum systems whose components are modelled by Wigner matrices. '
acknowledgement: The first author is supported in part by Hong Kong RGC Grant GRF
16301519 and NSFC 11871425. The second author is supported in part by ERC Advanced
Grant RANMAT 338804. The third author is supported in part by Swedish Research Council
Grant VR-2017-05195 and the Knut and Alice Wallenberg Foundation
article_number: e44
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Zhigang
full_name: Bao, Zhigang
id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
last_name: Bao
orcid: 0000-0003-3036-1475
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Kevin
full_name: Schnelli, Kevin
id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
last_name: Schnelli
orcid: 0000-0003-0954-3231
citation:
ama: Bao Z, Erdös L, Schnelli K. Equipartition principle for Wigner matrices. Forum
of Mathematics, Sigma. 2021;9. doi:10.1017/fms.2021.38
apa: Bao, Z., Erdös, L., & Schnelli, K. (2021). Equipartition principle for
Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press.
https://doi.org/10.1017/fms.2021.38
chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Equipartition Principle
for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge University
Press, 2021. https://doi.org/10.1017/fms.2021.38.
ieee: Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,”
Forum of Mathematics, Sigma, vol. 9. Cambridge University Press, 2021.
ista: Bao Z, Erdös L, Schnelli K. 2021. Equipartition principle for Wigner matrices.
Forum of Mathematics, Sigma. 9, e44.
mla: Bao, Zhigang, et al. “Equipartition Principle for Wigner Matrices.” Forum
of Mathematics, Sigma, vol. 9, e44, Cambridge University Press, 2021, doi:10.1017/fms.2021.38.
short: Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021).
date_created: 2021-06-13T22:01:33Z
date_published: 2021-05-27T00:00:00Z
date_updated: 2026-04-07T08:36:39Z
day: '27'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1017/fms.2021.38
ec_funded: 1
external_id:
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- '2008.07061'
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grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Forum of Mathematics, Sigma
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eissn:
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title: Equipartition principle for Wigner matrices
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...