---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '20478'
abstract:
- lang: eng
text: 'We consider the Wigner minor process, i.e. the eigenvalues of an N\times
N Wigner matrix H^{(N)} together with the eigenvalues of all its n\times n minors,
H^{(n)}, n\le N. The top eigenvalues of H^{(N)} and those of its immediate minor
H^{(N-1)} are very strongly correlated, but this correlation becomes weaker for
smaller minors H^{(N-k)} as k increases. For the GUE minor process the critical
transition regime around k\sim N^{2/3} was analyzed by Forrester and Nagao (J.
Stat. Mech.: Theory and Experiment, 2011) providing an explicit formula for the
nontrivial joint correlation function. We prove that this formula is universal,
i.e. it holds for the Wigner minor process. Moreover, we give a complete analysis
of the sub- and supercritical regimes both for eigenvalues and for the corresponding
eigenvector overlaps, thus we prove the decorrelation transition in full generality.'
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). Zhigang Bao Supported by Hong Kong RGC Grant GRF 16304724, NSFC12222121
and NSFC12271475. László Erdős, Joscha Henheik and Oleksii Kolupaiev Supported by
the ERC Advanced Grant “RMTBeyond” No. 101020331.
article_processing_charge: Yes (via OA deal)
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: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- first_name: Oleksii
full_name: Kolupaiev, Oleksii
id: 149b70d4-896a-11ed-bdf8-8c63fd44ca61
last_name: Kolupaiev
orcid: 0000-0003-1491-4623
citation:
ama: Bao Z, Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Decorrelation transition
in the Wigner minor process. Probability Theory and Related Fields. 2025.
doi:10.1007/s00440-025-01422-4
apa: Bao, Z., Cipolloni, G., Erdös, L., Henheik, S. J., & Kolupaiev, O. (2025).
Decorrelation transition in the Wigner minor process. Probability Theory and
Related Fields. Springer Nature. https://doi.org/10.1007/s00440-025-01422-4
chicago: Bao, Zhigang, Giorgio Cipolloni, László Erdös, Sven Joscha Henheik, and
Oleksii Kolupaiev. “Decorrelation Transition in the Wigner Minor Process.” Probability
Theory and Related Fields. Springer Nature, 2025. https://doi.org/10.1007/s00440-025-01422-4.
ieee: Z. Bao, G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Decorrelation
transition in the Wigner minor process,” Probability Theory and Related Fields.
Springer Nature, 2025.
ista: Bao Z, Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2025. Decorrelation
transition in the Wigner minor process. Probability Theory and Related Fields.
mla: Bao, Zhigang, et al. “Decorrelation Transition in the Wigner Minor Process.”
Probability Theory and Related Fields, Springer Nature, 2025, doi:10.1007/s00440-025-01422-4.
short: Z. Bao, G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Probability Theory
and Related Fields (2025).
corr_author: '1'
date_created: 2025-10-16T13:10:26Z
date_published: 2025-09-20T00:00:00Z
date_updated: 2026-06-18T18:23:40Z
day: '20'
ddc:
- '500'
department:
- _id: LaEr
doi: 10.1007/s00440-025-01422-4
ec_funded: 1
external_id:
arxiv:
- '2503.06549'
isi:
- '001574640900001'
fulldoi: https://doi.org/10.1007/s00440-025-01422-4
isi: 1
language:
- iso: eng
main_file_link:
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url: https://doi.org/10.1007/s00440-025-01422-4
month: '09'
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: Probability Theory and Related Fields
publication_identifier:
eissn:
- 1432-2064
issn:
- 0178-8051
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Decorrelation transition in the Wigner minor process
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
OA_place: repository
_id: '20576'
abstract:
- lang: eng
text: We prove that a very general class of $N\times N$ Hermitian random band matrices
is in the delocalized phase when the band width $W$ exceeds the critical threshold,
$W\gg \sqrt{N}$. In this regime, we show that, in the bulk spectrum, the eigenfunctions
are fully delocalized, the eigenvalues follow the universal Wigner-Dyson statistics,
and quantum unique ergodicity holds for general diagonal observables with an optimal
convergence rate. Our results are valid for general variance profiles, arbitrary
single entry distributions, in both real-symmetric and complex-Hermitian symmetry
classes. In particular, our work substantially generalizes the recent breakthrough
result of Yau and Yin [arXiv:2501.01718], obtained for a specific complex Hermitian
Gaussian block band matrix. The main technical input is the optimal multi-resolvent
local laws -- both in the averaged and fully isotropic form. We also generalize
the $\sqrtη$-rule from [arXiv:2012.13215] to exploit the additional effect of
traceless observables. Our analysis is based on the zigzag strategy, complemented
with a new global-scale estimate derived using the static version of the master
inequalities, while the zig-step and the a priori estimates on the deterministic
approximations are proven dynamically.
acknowledgement: " Supported by the ERC\r\nAdvanced Grant ”RMTBeyond” No. 101020331."
article_processing_charge: No
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. The zigzag strategy for random band matrices. arXiv.
doi:10.48550/ARXIV.2506.06441
apa: Erdös, L., & Riabov, V. (n.d.). The zigzag strategy for random band matrices.
arXiv. https://doi.org/10.48550/ARXIV.2506.06441
chicago: Erdös, László, and Volodymyr Riabov. “The Zigzag Strategy for Random Band
Matrices.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2506.06441.
ieee: L. Erdös and V. Riabov, “The zigzag strategy for random band matrices,” arXiv.
.
ista: Erdös L, Riabov V. The zigzag strategy for random band matrices. arXiv, 10.48550/ARXIV.2506.06441.
mla: Erdös, László, and Volodymyr Riabov. “The Zigzag Strategy for Random Band Matrices.”
ArXiv, doi:10.48550/ARXIV.2506.06441.
short: L. Erdös, V. Riabov, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-10-29T19:09:03Z
date_published: 2025-06-06T00:00:00Z
date_updated: 2026-04-07T12:32:19Z
day: '06'
department:
- _id: GradSch
- _id: LaEr
doi: 10.48550/ARXIV.2506.06441
ec_funded: 1
fulldoi: https://doi.org/10.48550/ARXIV.2506.06441
language:
- iso: eng
main_file_link:
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url: https://doi.org/10.48550/arXiv.2506.06441
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: arXiv
publication_status: draft
related_material:
record:
- id: '20575'
relation: dissertation_contains
status: public
status: public
title: The zigzag strategy for random band matrices
type: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '22340'
abstract:
- lang: eng
text: We show that Laplace isospectral deformations within a conformal class of
generic Liouville metrics on the two-dimensional torus that are linear in the
deformation parameter are necessarily trivial. Two of the main ingredients in
our proof are a noncancellation result for the wave trace and an analysis of the
second order variational formula for the energy functional associated to closed
geodesics. Noncancellation allows us to detect parts of the length spectrum from
the Laplace spectrum and conclude rational integrability for the deformed geodesic
flow (Liouville metrics are folklorically conjectured to be the only Riemannian
metrics with integrable geodesic flow on the torus). We then use the second variational
formula to show how the preservation of a single rational torus is sufficient
to conclude triviality of the deformation, assuming linearity. We also present
some evidence that our hypothesis of linearity may indeed be necessary.
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: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Yunzhe
full_name: Li, Yunzhe
id: 41cb05d3-f128-11eb-9611-e4e2b3cfba31
last_name: Li
- first_name: Amir
full_name: Vig, Amir
id: 49d58dd5-45f5-11ec-9f86-8ce1276989b9
last_name: Vig
citation:
ama: Henheik SJ, Kaloshin V, Li Y, Vig A. Spectral rigidity of Liouville tori. arXiv.
doi:10.48550/ARXIV.2511.10398
apa: Henheik, S. J., Kaloshin, V., Li, Y., & Vig, A. (n.d.). Spectral rigidity
of Liouville tori. arXiv. https://doi.org/10.48550/ARXIV.2511.10398
chicago: Henheik, Sven Joscha, Vadim Kaloshin, Yunzhe Li, and Amir Vig. “Spectral
Rigidity of Liouville Tori.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2511.10398.
ieee: S. J. Henheik, V. Kaloshin, Y. Li, and A. Vig, “Spectral rigidity of Liouville
tori,” arXiv. .
ista: Henheik SJ, Kaloshin V, Li Y, Vig A. Spectral rigidity of Liouville tori.
arXiv, 10.48550/ARXIV.2511.10398.
mla: Henheik, Sven Joscha, et al. “Spectral Rigidity of Liouville Tori.” ArXiv,
doi:10.48550/ARXIV.2511.10398.
short: S.J. Henheik, V. Kaloshin, Y. Li, A. Vig, ArXiv (n.d.).
corr_author: '1'
date_created: 2026-07-14T12:51:50Z
date_published: 2025-11-13T00:00:00Z
date_updated: 2026-07-20T14:58:23Z
day: '13'
department:
- _id: VaKa
- _id: LaEr
doi: 10.48550/ARXIV.2511.10398
external_id:
arxiv:
- '2511.10398'
fulldoi: https://doi.org/10.48550/ARXIV.2511.10398
keyword:
- Differential Geometry (math.DG)
- Mathematical Physics (math-ph)
- Dynamical Systems (math.DS)
- Spectral Theory (math.SP)
- 'FOS: Mathematics'
- 'FOS: Mathematics'
- 'FOS: Physical sciences'
- 'FOS: Physical sciences'
- 58J42
- 37J35
- 37J35
- 35P20
- 58J40
- 58J50
- 37D40
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2511.10398
month: '11'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: draft
related_material:
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status: public
title: Spectral rigidity of Liouville tori
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: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '18112'
abstract:
- lang: eng
text: 'It is conjectured that the only integrable metrics on the two-dimensional
torus are Liouville metrics. In this paper, we study a deformative version of
this conjecture: we consider integrable deformations of a non-flat Liouville metric
in a conformal class and show that for a fairly large class of such deformations,
the deformed metric is again Liouville. The principal idea of the argument is
that the preservation of rational invariant tori in the foliation of the phase
space forces a linear combination on the Fourier coefficients of the deformation
to vanish. Showing that the resulting linear system is non-degenerate will then
yield the claim. Since our method of proof immediately carries over to higher
dimensional tori, we obtain analogous statements in this more general case. To
put our results in perspective, we review existing results about integrable metrics
on the torus.'
acknowledgement: I am very grateful to Vadim Kaloshin for suggesting the topic, his
guidance during this project, and many helpful comments on an earlier version of
the manuscript. Moreover, I would like to thank Comlan Edmond Koudjinan and Volodymyr
Riabov for interesting discussions. Partial financial support by the ERC Advanced
Grant ‘RMTBeyond’ No. 101020331 is gratefully acknowledged. This project received
funding from the European Research Council (ERC) ERC Grant No. 885707.
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
citation:
ama: Henheik SJ. Deformational rigidity of integrable metrics on the torus. Ergodic
Theory and Dynamical Systems. 2025;45(2):467-503. doi:10.1017/etds.2024.48
apa: Henheik, S. J. (2025). Deformational rigidity of integrable metrics on the
torus. Ergodic Theory and Dynamical Systems. Cambridge University Press.
https://doi.org/10.1017/etds.2024.48
chicago: Henheik, Sven Joscha. “Deformational Rigidity of Integrable Metrics on
the Torus.” Ergodic Theory and Dynamical Systems. Cambridge University
Press, 2025. https://doi.org/10.1017/etds.2024.48.
ieee: S. J. Henheik, “Deformational rigidity of integrable metrics on the torus,”
Ergodic Theory and Dynamical Systems, vol. 45, no. 2. Cambridge University
Press, pp. 467–503, 2025.
ista: Henheik SJ. 2025. Deformational rigidity of integrable metrics on the torus.
Ergodic Theory and Dynamical Systems. 45(2), 467–503.
mla: Henheik, Sven Joscha. “Deformational Rigidity of Integrable Metrics on the
Torus.” Ergodic Theory and Dynamical Systems, vol. 45, no. 2, Cambridge
University Press, 2025, pp. 467–503, doi:10.1017/etds.2024.48.
short: S.J. Henheik, Ergodic Theory and Dynamical Systems 45 (2025) 467–503.
corr_author: '1'
date_created: 2024-09-22T22:01:43Z
date_published: 2025-02-01T00:00:00Z
date_updated: 2026-07-29T13:18:16Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1017/etds.2024.48
ec_funded: 1
external_id:
isi:
- '001308182000001'
file:
- access_level: open_access
checksum: 650fe115d998fe0ac3a8d0c7519447c8
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date_created: 2025-01-13T08:51:40Z
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isi: 1
issue: '2'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 467-503
project:
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call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
- _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A
call_identifier: H2020
grant_number: '885707'
name: Spectral rigidity and integrability for billiards and geodesic flows
publication: Ergodic Theory and Dynamical Systems
publication_identifier:
eissn:
- 1469-4417
issn:
- 0143-3857
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
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scopus_import: '1'
status: public
title: Deformational rigidity of integrable metrics on the torus
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: 45
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '19001'
abstract:
- lang: eng
text: We consider two Hamiltonians that are close to each other, H1≈H2, and analyze
the time-decay of the corresponding Loschmidt echo M(t):=|⟨ψ0,eitH2e−itH1ψ0⟩|2
that expresses the effect of an imperfect time reversal on the initial state ψ0.
Our model Hamiltonians are deformed Wigner matrices that do not share a common
eigenbasis. The main tools for our results are two-resolvent laws for such H1
and H2.
acknowledgement: We thank Giorgio Cipolloni for helpful discussions in a closely related
joint project. Open access funding provided by Institute of Science and Technology
(IST Austria). All authors were supported by the ERC Advanced Grant “RMTBeyond”
No. 101020331.
article_number: '14'
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: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- first_name: Oleksii
full_name: Kolupaiev, Oleksii
id: 149b70d4-896a-11ed-bdf8-8c63fd44ca61
last_name: Kolupaiev
orcid: 0000-0003-1491-4623
citation:
ama: Erdös L, Henheik SJ, Kolupaiev O. Loschmidt echo for deformed Wigner matrices.
Letters in Mathematical Physics. 2025;115. doi:10.1007/s11005-025-01904-5
apa: Erdös, L., Henheik, S. J., & Kolupaiev, O. (2025). Loschmidt echo for deformed
Wigner matrices. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-025-01904-5
chicago: Erdös, László, Sven Joscha Henheik, and Oleksii Kolupaiev. “Loschmidt Echo
for Deformed Wigner Matrices.” Letters in Mathematical Physics. Springer
Nature, 2025. https://doi.org/10.1007/s11005-025-01904-5.
ieee: L. Erdös, S. J. Henheik, and O. Kolupaiev, “Loschmidt echo for deformed Wigner
matrices,” Letters in Mathematical Physics, vol. 115. Springer Nature,
2025.
ista: Erdös L, Henheik SJ, Kolupaiev O. 2025. Loschmidt echo for deformed Wigner
matrices. Letters in Mathematical Physics. 115, 14.
mla: Erdös, László, et al. “Loschmidt Echo for Deformed Wigner Matrices.” Letters
in Mathematical Physics, vol. 115, 14, Springer Nature, 2025, doi:10.1007/s11005-025-01904-5.
short: L. Erdös, S.J. Henheik, O. Kolupaiev, Letters in Mathematical Physics 115
(2025).
corr_author: '1'
date_created: 2025-02-05T06:48:29Z
date_published: 2025-01-30T00:00:00Z
date_updated: 2026-07-29T13:18:16Z
day: '30'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s11005-025-01904-5
ec_funded: 1
external_id:
arxiv:
- '2410.08108'
isi:
- '001409618800002'
pmid:
- '39896265'
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checksum: ee07edf5f85a6f2651926b2f8760af74
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call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Letters in Mathematical Physics
publication_identifier:
issn:
- 1573-0530
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
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relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Loschmidt echo 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: 115
year: '2025'
...
---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
_id: '19548'
abstract:
- lang: eng
text: "We consider the BCS energy gap „.T / (essentially given by „.T / \x19 \x81.T;
p\x16/,\r\nthe BCS order parameter) at all temperatures 0 \x14 T \x14 Tc up to
the critical one, Tc, and show\r\nthat, in the limit of weak coupling, the ratio
„.T /=Tc is given by a universal function of the relative temperature T =Tc. On
the one hand, this recovers a recent result by Langmann and Triola\r\n[Phys. Rev.
B 108 (2023), no. 10, article no. 104503] on three-dimensional s-wave superconductors
for temperatures bounded uniformly away from Tc. On the other hand, our result
lifts these\r\nrestrictions, as we consider arbitrary spatial dimensions d 2 ¹1;
2; 3º, discuss superconductors\r\nwith non-zero angular momentum (primarily in
two dimensions), and treat the perhaps physically most interesting (due to the
occurrence of the superconducting phase transition) regime of\r\ntemperatures
close to Tc.\r\n\r\n\r\n ."
acknowledgement: "We thank Andreas Deuchert, Christian Hainzl, Edwin Langmann, Marius
Lemm, Robert Seiringer, and Jan Philip Solovej for helpful discussions,\r\nand Edwin
Langmann and Robert Seiringer for valuable comments on an earlier version of the
manuscript.\r\nFunding. Joscha Henheik gratefully acknowledges partial financial
support by the\r\nERC Advanced Grant “RMTBeyond” No. 101020331. Asbjørn Bækgaard
Lauritsen\r\ngratefully acknowledges partial financial support by the Austrian Science
Fund (FWF)\r\nthrough grant DOI 10.55776/I6427 (as part of the SFB/TRR 352).\r\n"
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: 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. Universal behavior of the BCS energy gap. Journal
of Spectral Theory. 2025;15(1):305–352. doi:10.4171/JST/540
apa: Henheik, S. J., & Lauritsen, A. B. (2025). Universal behavior of the BCS
energy gap. Journal of Spectral Theory. EMS Press. https://doi.org/10.4171/JST/540
chicago: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “Universal Behavior
of the BCS Energy Gap.” Journal of Spectral Theory. EMS Press, 2025. https://doi.org/10.4171/JST/540.
ieee: S. J. Henheik and A. B. Lauritsen, “Universal behavior of the BCS energy gap,”
Journal of Spectral Theory, vol. 15, no. 1. EMS Press, pp. 305–352, 2025.
ista: Henheik SJ, Lauritsen AB. 2025. Universal behavior of the BCS energy gap.
Journal of Spectral Theory. 15(1), 305–352.
mla: Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “Universal Behavior of
the BCS Energy Gap.” Journal of Spectral Theory, vol. 15, no. 1, EMS Press,
2025, pp. 305–352, doi:10.4171/JST/540.
short: S.J. Henheik, A.B. Lauritsen, Journal of Spectral Theory 15 (2025) 305–352.
corr_author: '1'
date_created: 2025-04-11T09:19:28Z
date_published: 2025-01-09T00:00:00Z
date_updated: 2026-07-29T13:18:17Z
day: '09'
ddc:
- '500'
department:
- _id: LaEr
- _id: RoSe
doi: 10.4171/JST/540
ec_funded: 1
external_id:
arxiv:
- '2312.11310'
isi:
- '001438931600009'
file:
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checksum: f49e06e8dba819f7ad52a202e287ebca
content_type: application/pdf
creator: cchlebak
date_created: 2025-04-11T09:13:31Z
date_updated: 2025-04-11T09:13:31Z
file_id: '19549'
file_name: Henheik_JSpectralTheory_2025.pdf
file_size: 779158
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success: 1
file_date_updated: 2025-04-11T09:13:31Z
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intvolume: ' 15'
isi: 1
issue: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 305–352
project:
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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: Journal of Spectral Theory
publication_identifier:
eissn:
- 1664-0403
publication_status: published
publisher: EMS Press
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related_material:
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relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Universal behavior of the BCS energy gap
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: 15
year: '2025'
...
---
OA_place: repository
_id: '19552'
abstract:
- lang: eng
text: "Particle creation terms in quantum Hamiltonians are usually ultraviolet\r\ndivergent
and thus mathematically ill defined. A rather novel way of solving\r\nthis problem
is based on imposing so-called interior-boundary conditions on the\r\nwave function.
Previous papers showed that this approach works in the\r\nnon-relativistic regime,
but particle creation is mostly relevant in the\r\nrelativistic case after all.
In flat relativistic space-time (that is,\r\nneglecting gravity), the approach
was previously found to work only for certain\r\nsomewhat artificial cases. Here,
as a way of taking gravity into account, we\r\nconsider curved space-time, specifically
the super-critical\r\nReissner-Nordstr\\\"om space-time, which features a naked
timelike singularity.\r\nWe find that the interior-boundary approach works fully
in this setting; in\r\nparticular, we prove rigorously the existence of well-defined,
self-adjoint\r\nHamiltonians with particle creation at the singularity, based
on\r\ninterior-boundary conditions. We also non-rigorously analyze the asymptotic\r\nbehavior
of the Bohmian trajectories and construct the corresponding Bohm-Bell\r\nprocess
of particle creation, motion, and annihilation. The upshot is that in\r\nquantum
physics, a naked space-time singularity need not lead to a breakdown of\r\nphysical
laws, but on the contrary allows for boundary conditions governing\r\nwhat comes
out of the singularity and thereby removing the ultraviolet\r\ndivergence."
acknowledgement: "JH gratefully acknowledges partial financial support by the ERC
Advanced\r\nGrant “RMTBeyond” No. 101020331."
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: Bipul
full_name: Poudyal, Bipul
last_name: Poudyal
- first_name: Roderich
full_name: Tumulka, Roderich
last_name: Tumulka
citation:
ama: Henheik SJ, Poudyal B, Tumulka R. How a space-time singularity helps remove
the ultraviolet divergence problem. arXiv. doi:10.48550/arXiv.2409.00677
apa: Henheik, S. J., Poudyal, B., & Tumulka, R. (n.d.). How a space-time singularity
helps remove the ultraviolet divergence problem. arXiv. https://doi.org/10.48550/arXiv.2409.00677
chicago: Henheik, Sven Joscha, Bipul Poudyal, and Roderich Tumulka. “How a Space-Time
Singularity Helps Remove the Ultraviolet Divergence Problem.” ArXiv, n.d.
https://doi.org/10.48550/arXiv.2409.00677.
ieee: S. J. Henheik, B. Poudyal, and R. Tumulka, “How a space-time singularity helps
remove the ultraviolet divergence problem,” arXiv. .
ista: Henheik SJ, Poudyal B, Tumulka R. How a space-time singularity helps remove
the ultraviolet divergence problem. arXiv, 10.48550/arXiv.2409.00677.
mla: Henheik, Sven Joscha, et al. “How a Space-Time Singularity Helps Remove the
Ultraviolet Divergence Problem.” ArXiv, doi:10.48550/arXiv.2409.00677.
short: S.J. Henheik, B. Poudyal, R. Tumulka, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-04-11T12:07:25Z
date_published: 2025-02-28T00:00:00Z
date_updated: 2026-07-29T13:18:16Z
day: '28'
department:
- _id: LaEr
doi: 10.48550/arXiv.2409.00677
ec_funded: 1
external_id:
arxiv:
- '2409.00677'
fulldoi: https://doi.org/10.48550/arXiv.2409.00677
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2409.00677
month: '02'
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: How a space-time singularity helps remove the ultraviolet divergence problem
type: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2025'
...
---
OA_place: repository
_id: '19546'
abstract:
- lang: eng
text: "We study the sensitivity of the eigenvectors of random matrices, showing
that\r\neven small perturbations make the eigenvectors almost orthogonal. More\r\nprecisely,
we consider two deformed Wigner matrices $W+D_1$, $W+D_2$ and show\r\nthat their
bulk eigenvectors become asymptotically orthogonal as soon as\r\n$\\mathrm{Tr}(D_1-D_2)^2\\gg
1$, or their respective energies are separated on a\r\nscale much bigger than
the local eigenvalue spacing. Furthermore, we show that\r\nquadratic forms of
eigenvectors of $W+D_1$, $W+D_2$ with any deterministic\r\nmatrix $A\\in\\mathbf{C}^{N\\times
N}$ in a specific subspace of codimension one\r\nare of size $N^{-1/2}$. This
proves a generalization of the Eigenstate\r\nThermalization Hypothesis to eigenvectors
belonging to two different spectral\r\nfamilies."
acknowledgement: Supported by the 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
- first_name: Oleksii
full_name: Kolupaiev, Oleksii
id: 149b70d4-896a-11ed-bdf8-8c63fd44ca61
last_name: Kolupaiev
orcid: 0000-0003-1491-4623
citation:
ama: Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Eigenvector decorrelation for
random matrices. arXiv. doi:10.48550/arXiv.2410.10718
apa: Cipolloni, G., Erdös, L., Henheik, S. J., & Kolupaiev, O. (n.d.). Eigenvector
decorrelation for random matrices. arXiv. https://doi.org/10.48550/arXiv.2410.10718
chicago: Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev.
“Eigenvector Decorrelation for Random Matrices.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2410.10718.
ieee: G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Eigenvector decorrelation
for random matrices,” arXiv. .
ista: Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Eigenvector decorrelation for
random matrices. arXiv, 10.48550/arXiv.2410.10718.
mla: Cipolloni, Giorgio, et al. “Eigenvector Decorrelation for Random Matrices.”
ArXiv, doi:10.48550/arXiv.2410.10718.
short: G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-04-11T08:34:49Z
date_published: 2025-01-30T00:00:00Z
date_updated: 2026-09-16T10:00:54Z
day: '30'
department:
- _id: LaEr
doi: 10.48550/arXiv.2410.10718
ec_funded: 1
external_id:
arxiv:
- '2410.10718'
fulldoi: https://doi.org/10.48550/arXiv.2410.10718
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2410.10718
month: '01'
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
- id: '22923'
relation: later_version
status: public
status: public
title: Eigenvector decorrelation 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: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2025'
...
---
OA_place: publisher
_id: '20575'
abstract:
- lang: eng
text: "This thesis deals with eigenvalue and eigenvector universality results for
random matrix ensembles equipped with non-trivial spatial structure. We consider
both mean-field models with a general variance profile (Wigner-type matrices)
and correlation structure (correlated matrices) among the entries, as well as
non-mean-field random band matrices with bandwidth W >> N^(1/2).\r\n\r\nTo extract
the universal properties of random matrix spectra and eigenvectors, we obtain
concentration estimates for their resolvent, the local laws, which generalize
the celebrated Wigner semicircle law for a broad class of random matrices to much
finer spectral scales. The local laws hold for both a single resolvent as well
as for products of multiple resolvents, known as resolvent chains, and express
the remarkable approximately-deterministic behavior of these objects down to the
microscopic scale.\r\n\r\nOur primary tool for establishing the local laws is
the dynamical Zigzag strategy, which we develop in the setting of spatially-inhomogeneous
random matrices. Our proof method systematically addresses the challenges arising
from non-trivial spatial structures and is robust to all types of singularities
in the spectrum, as we demonstrate in the correlated setting. Furthermore, we
incorporate the analysis of the deterministic resolvent chain approximations into
the dynamical framework of the Zigzag strategy, synthesizing a unified toolkit
for establishing multi-resolvent local laws.\r\n\r\nUsing these methods, we prove
complete eigenvector delocalization, the Eigenstate Thermalization Hypothesis,
and Wigner-Dyson universality in the bulk for random band matrices down to the
optimal bandwidth W >> N^(1/2). For mean-field ensembles, we establish universality
of local eigenvalue statistics at the cups for random matrices with correlated
entries, and the Eigenstate Thermalization Hypothesis for Wigner-type matrices
in the bulk of the spectrum.\r\n\r\nFinally, this thesis also contains other applications
of the multi-resolvent local laws to spatially-inhomogeneous random matrices,
obtained prior to the development of the Zigzag strategy. In particular, we provide
a complete analysis of mesoscopic linear-eigenvalue statistics of Wigner-type
matrices in all spectral regimes, including the novel cusps, and rigorously establish
the prethermalization phenomenon for deformed Wigner matrices.\r\n\r\nThe main
body of this thesis consists of seven research papers (listed on page xi), each
presented in a separate chapter with its own introduction and all relevant context,
suitable to be read independently. We ask the reader’s indulgence for the repetitions
in the historical overviews and other minor redundancies that remain among the
chapters as a result. The overall Introduction, preceding the chapters, provides
a condensed, informal summary of the main ideas and concepts at the core of these
works.\r\n"
acknowledgement: "The work comprising this thesis was supported by the ERC Advanced
Grant \"RMTBeyond\"\r\nNo.101020331 awarded to my advisor."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Volodymyr
full_name: Riabov, Volodymyr
id: 1949f904-edfb-11eb-afb5-e2dfddabb93b
last_name: Riabov
citation:
ama: Riabov V. Universality in random matrices with spatial structure. 2025. doi:10.15479/AT-ISTA-20575
apa: Riabov, V. (2025). Universality in random matrices with spatial structure.
Institute of Science and Technology Austria. https://doi.org/10.15479/AT-ISTA-20575
chicago: Riabov, Volodymyr. “Universality in Random Matrices with Spatial Structure.”
Institute of Science and Technology Austria, 2025. https://doi.org/10.15479/AT-ISTA-20575.
ieee: V. Riabov, “Universality in random matrices with spatial structure,” Institute
of Science and Technology Austria, 2025.
ista: Riabov V. 2025. Universality in random matrices with spatial structure. Institute
of Science and Technology Austria.
mla: Riabov, Volodymyr. Universality in Random Matrices with Spatial Structure.
Institute of Science and Technology Austria, 2025, doi:10.15479/AT-ISTA-20575.
short: V. Riabov, Universality in Random Matrices with Spatial Structure, Institute
of Science and Technology Austria, 2025.
corr_author: '1'
date_created: 2025-10-29T19:12:24Z
date_published: 2025-11-03T00:00:00Z
date_updated: 2026-10-16T08:41:47Z
day: '3'
ddc:
- '515'
- '519'
degree_awarded: PhD
department:
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- _id: LaEr
doi: 10.15479/AT-ISTA-20575
ec_funded: 1
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date_created: 2025-10-29T18:54:53Z
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file_size: 17841612
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has_accepted_license: '1'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: '436'
project:
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call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication_identifier:
isbn:
- 978-3-99078-064-0
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
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- id: '19368'
relation: part_of_dissertation
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- id: '20576'
relation: part_of_dissertation
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- id: '17174'
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- id: '19547'
relation: part_of_dissertation
status: public
- id: '19598'
relation: part_of_dissertation
status: public
- id: '18554'
relation: part_of_dissertation
status: public
- id: '18764'
relation: part_of_dissertation
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: Universality in random matrices with spatial structure
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: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2025'
...
---
OA_place: publisher
_id: '19540'
abstract:
- lang: eng
text: "This thesis deals with several different models for complex quantum mechanical
systems and is structured in three main parts. \r\n\t\r\nIn Part I, we study mean
field random matrices as models for quantum Hamiltonians. Our focus lies on proving
concentration estimates for resolvents of random matrices, so-called local laws,
mostly in the setting of multiple resolvents. These estimates have profound consequences
for eigenvector overlaps and thermalization problems. More concretely, we obtain,
e.g., the optimal eigenstate thermalization hypothesis (ETH) uniformly in the
spectrum for Wigner matrices, an optimal lower bound on non-Hermitian eigenvector
overlaps, and prethermalization for deformed Wigner matrices.\tIn order to prove
our novel multi-resolvent local laws, we develop and devise two main methods,
the static Psi-method and the dynamical Zigzag strategy. \r\n\t\r\nIn Part II,
we study Bardeen-Cooper-Schrieffer (BCS) theory, the standard mean field microscopic
theory of superconductivity. We focus on asymptotic formulas for the characteristic
critical temperature and energy gap of a superconductor and prove universality
of their ratio in various physical regimes. Additionally, we investigate multi-band
superconductors and show that inter-band coupling effects can only enhance the
critical temperature. \r\n\t\r\nIn Part III, we study quantum lattice systems.
On the one hand, we show a strong version of the local-perturbations-perturb-locally
(LPPL) principle for the ground state of weakly interacting quantum spin systems
with a uniform on-site gap. On the other hand, we introduce a notion of a local
gap and rigorously justify response theory and the Kubo formula under the weakened
assumption of a local gap. \r\n\t\r\nAdditionally, we discuss two classes of problems
which do not fit into the three main parts of the thesis. These are deformational
rigidity of Liouville metrics on the torus and relativistic toy models of particle
creation via interior-boundary-conditions (IBCs). "
alternative_title:
- ISTA Thesis
article_processing_charge: No
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. Modeling complex quantum systems: Random matrices, BCS theory,
and quantum lattice systems. 2025. doi:10.15479/AT-ISTA-19540'
apa: 'Henheik, S. J. (2025). Modeling complex quantum systems: Random matrices,
BCS theory, and quantum lattice systems. Institute of Science and Technology
Austria. https://doi.org/10.15479/AT-ISTA-19540'
chicago: 'Henheik, Sven Joscha. “Modeling Complex Quantum Systems: Random Matrices,
BCS Theory, and Quantum Lattice Systems.” Institute of Science and Technology
Austria, 2025. https://doi.org/10.15479/AT-ISTA-19540.'
ieee: 'S. J. Henheik, “Modeling complex quantum systems: Random matrices, BCS theory,
and quantum lattice systems,” Institute of Science and Technology Austria, 2025.'
ista: 'Henheik SJ. 2025. Modeling complex quantum systems: Random matrices, BCS
theory, and quantum lattice systems. Institute of Science and Technology Austria.'
mla: 'Henheik, Sven Joscha. Modeling Complex Quantum Systems: Random Matrices,
BCS Theory, and Quantum Lattice Systems. Institute of Science and Technology
Austria, 2025, doi:10.15479/AT-ISTA-19540.'
short: 'S.J. Henheik, Modeling Complex Quantum Systems: Random Matrices, BCS Theory,
and Quantum Lattice Systems, Institute of Science and Technology Austria, 2025.'
corr_author: '1'
date_created: 2025-04-10T21:21:18Z
date_published: 2025-04-10T00:00:00Z
date_updated: 2026-10-16T08:41:47Z
day: '10'
ddc:
- '519'
degree_awarded: PhD
department:
- _id: GradSch
- _id: LaEr
doi: 10.15479/AT-ISTA-19540
doi_confirm: '1'
ec_funded: 1
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checksum: b8477ae5578436c72c3bb4193ad34ac5
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creator: shenheik
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- 978-3-99078-057-2
issn:
- 2663-337X
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publisher: Institute of Science and Technology Austria
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supervisor:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
title: 'Modeling complex quantum systems: Random matrices, BCS theory, and quantum
lattice systems'
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legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: dissertation
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2025'
...
---
OA_place: publisher
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abstract:
- lang: eng
text: We prove that a class of weakly perturbed Hamiltonians of the form H_λ= H_0
+ λW, with W being a Wigner matrix, exhibits prethermalization. That is, the time
evolution generated by H_λ relaxes to its ultimate thermal state via an intermediate
prethermal state with a lifetime of order λ^{-2}. Moreover, we obtain a general
relaxation formula, expressing the perturbed dynamics via the unperturbed dynamics
and the ultimate thermal state. The proof relies on a two-resolvent law for the
deformed Wigner matrix H_λ.
acknowledgement: "All authors were supported by the ERC Advanced Grant “RMTBeyond”
No. 101020331.\r\nJ.R. was additionally supported by the ERC Advanced Grant “LDRaM”
No. 884584.\r\nWe thank Peter Reimann and Lennart Dabelow for helpful comments.
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: 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: Jana
full_name: Reker, Jana
id: e796e4f9-dc8d-11ea-abe3-97e26a0323e9
last_name: Reker
- first_name: Volodymyr
full_name: Riabov, Volodymyr
id: 1949f904-edfb-11eb-afb5-e2dfddabb93b
last_name: Riabov
citation:
ama: Erdös L, Henheik SJ, Reker J, Riabov V. Prethermalization for deformed Wigner
matrices. Annales Henri Poincare. 2025;26:1991-2033. doi:10.1007/s00023-024-01518-y
apa: Erdös, L., Henheik, S. J., Reker, J., & Riabov, V. (2025). Prethermalization
for deformed Wigner matrices. Annales Henri Poincare. Springer Nature.
https://doi.org/10.1007/s00023-024-01518-y
chicago: Erdös, László, Sven Joscha Henheik, Jana Reker, and Volodymyr Riabov. “Prethermalization
for Deformed Wigner Matrices.” Annales Henri Poincare. Springer Nature,
2025. https://doi.org/10.1007/s00023-024-01518-y.
ieee: L. Erdös, S. J. Henheik, J. Reker, and V. Riabov, “Prethermalization for deformed
Wigner matrices,” Annales Henri Poincare, vol. 26. Springer Nature, pp.
1991–2033, 2025.
ista: Erdös L, Henheik SJ, Reker J, Riabov V. 2025. Prethermalization for deformed
Wigner matrices. Annales Henri Poincare. 26, 1991–2033.
mla: Erdös, László, et al. “Prethermalization for Deformed Wigner Matrices.” Annales
Henri Poincare, vol. 26, Springer Nature, 2025, pp. 1991–2033, doi:10.1007/s00023-024-01518-y.
short: L. Erdös, S.J. Henheik, J. Reker, V. Riabov, Annales Henri Poincare 26 (2025)
1991–2033.
corr_author: '1'
das_tickbox: '0'
date_created: 2025-01-05T23:01:59Z
date_published: 2025-06-01T00:00:00Z
date_updated: 2026-10-16T08:41:47Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00023-024-01518-y
ec_funded: 1
external_id:
arxiv:
- '2310.06677'
isi:
- '001385326500001'
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isi: 1
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 1991-2033
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call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Annales Henri Poincare
publication_identifier:
issn:
- 1424-0637
publication_status: published
publisher: Springer Nature
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supplementarymaterial: yes
title: Prethermalization 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 26
year: '2025'
...
---
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: 2026-07-29T13:18:16Z
day: '17'
department:
- _id: LaEr
doi: 10.48550/arXiv.2309.05488
ec_funded: 1
external_id:
arxiv:
- '2309.05488'
fulldoi: https://doi.org/10.48550/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: '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: 2026-07-29T13:18:16Z
day: '21'
department:
- _id: LaEr
- _id: RoSe
doi: 10.48550/arXiv.2409.17297
external_id:
arxiv:
- '2409.17297'
fulldoi: https://doi.org/10.48550/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: '22290'
relation: later_version
status: public
- 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: 2026-07-29T13:18:17Z
day: '03'
department:
- _id: LaEr
doi: 10.48550/arXiv.2410.06813
ec_funded: 1
external_id:
arxiv:
- '2410.06813'
fulldoi: https://doi.org/10.48550/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:
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relation: later_version
status: public
- id: '20575'
relation: dissertation_contains
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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: 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: 2026-07-29T13:18:16Z
day: '14'
department:
- _id: LaEr
doi: 10.48550/arXiv.2410.10809
external_id:
arxiv:
- '2410.10809'
fulldoi: https://doi.org/10.48550/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
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'
das_tickbox: '0'
date_created: 2024-05-23T08:31:57Z
date_published: 2024-04-01T00:00:00Z
date_updated: 2026-10-02T11:31:29Z
day: '01'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1142/s2010326324500072
ec_funded: 1
external_id:
arxiv:
- '2212.14638'
isi:
- '001229295200002'
fulldoi: https://doi.org/10.1142/s2010326324500072
intvolume: ' 13'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
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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'
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title: Dynamics of a rank-one multiplicative perturbation of a unitary matrix
type: journal_article
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volume: 13
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'
das_tickbox: '0'
date_created: 2023-11-15T23:48:14Z
date_published: 2024-10-01T00:00:00Z
date_updated: 2026-10-02T11:43:00Z
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
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file_id: '18786'
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file_date_updated: 2025-01-09T07:56:28Z
fulldoi: https://doi.org/10.1142/s0129055x2360005x
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:
record:
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relation: dissertation_contains
status: public
- id: '18135'
relation: dissertation_contains
status: public
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 36
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...
---
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'
das_tickbox: '1'
dataavailabilitystatement: There is no data associated to this work.
date_created: 2024-11-17T23:01:46Z
date_published: 2024-12-01T00:00:00Z
date_updated: 2026-10-16T08:34:30Z
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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creator: dernst
date_created: 2024-11-18T08:15:07Z
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language:
- iso: eng
month: '12'
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oa_version: Published Version
pmid: 1
publication: Communications in Mathematical Physics
publication_identifier:
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issn:
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publication_status: published
publisher: Springer Nature
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related_material:
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status: public
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scopus_import: '1'
status: public
supplementarymaterial: yes
title: Eigenstate Thermalization Hypothesis for Wigner-type 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: 405
year: '2024'
...
---
_id: '13975'
abstract:
- lang: eng
text: "We consider the spectrum of random Laplacian matrices of the form Ln=An−Dn
where An\r\n is a real symmetric random matrix and Dn is a diagonal matrix whose
entries are equal to the corresponding row sums of An. If An is a Wigner matrix
with entries in the domain of attraction of a Gaussian distribution, the empirical
spectral measure of Ln is known to converge to the free convolution of a semicircle
distribution and a standard real Gaussian distribution. We consider real symmetric
random matrices An with independent entries (up to symmetry) whose row sums converge
to a purely non-Gaussian infinitely divisible distribution, which fall into the
class of Lévy–Khintchine random matrices first introduced by Jung [Trans Am Math
Soc, 370, (2018)]. Our main result shows that the empirical spectral measure of
Ln converges almost surely to a deterministic limit. A key step in the proof
is to use the purely non-Gaussian nature of the row sums to build a random operator
to which Ln converges in an appropriate sense. This operator leads to a recursive
distributional equation uniquely describing the Stieltjes transform of the limiting
empirical spectral measure."
acknowledgement: "The first author thanks Yizhe Zhu for pointing out reference [30].
We thank David Renfrew for comments on an earlier draft. We thank the anonymous
referee for a careful reading and helpful comments.\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: 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
citation:
ama: Campbell AJ, O’Rourke S. Spectrum of Lévy–Khintchine random laplacian matrices.
Journal of Theoretical Probability. 2024;37:933-973. doi:10.1007/s10959-023-01275-4
apa: Campbell, A. J., & O’Rourke, S. (2024). Spectrum of Lévy–Khintchine random
laplacian matrices. Journal of Theoretical Probability. Springer Nature.
https://doi.org/10.1007/s10959-023-01275-4
chicago: Campbell, Andrew J, and Sean O’Rourke. “Spectrum of Lévy–Khintchine Random
Laplacian Matrices.” Journal of Theoretical Probability. Springer Nature,
2024. https://doi.org/10.1007/s10959-023-01275-4.
ieee: A. J. Campbell and S. O’Rourke, “Spectrum of Lévy–Khintchine random laplacian
matrices,” Journal of Theoretical Probability, vol. 37. Springer Nature,
pp. 933–973, 2024.
ista: Campbell AJ, O’Rourke S. 2024. Spectrum of Lévy–Khintchine random laplacian
matrices. Journal of Theoretical Probability. 37, 933–973.
mla: Campbell, Andrew J., and Sean O’Rourke. “Spectrum of Lévy–Khintchine Random
Laplacian Matrices.” Journal of Theoretical Probability, vol. 37, Springer
Nature, 2024, pp. 933–73, doi:10.1007/s10959-023-01275-4.
short: A.J. Campbell, S. O’Rourke, Journal of Theoretical Probability 37 (2024)
933–973.
corr_author: '1'
das_tickbox: '1'
dataavailabilitystatement: All data generated or analyzed during this study are included
in this published article.
date_created: 2023-08-06T22:01:13Z
date_published: 2024-03-01T00:00:00Z
date_updated: 2026-10-16T08:30:34Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s10959-023-01275-4
external_id:
arxiv:
- '2210.07927'
isi:
- '001038341000001'
file:
- access_level: open_access
checksum: f7793d313104c70422140c5e6494c779
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creator: dernst
date_created: 2024-07-22T09:41:21Z
date_updated: 2024-07-22T09:41:21Z
file_id: '17300'
file_name: 2024_JourTheorProbab_Campbell.pdf
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intvolume: ' 37'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 933-973
publication: Journal of Theoretical Probability
publication_identifier:
eissn:
- 1572-9230
issn:
- 0894-9840
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
researchdata_availability: yes (supplementary data)
scopus_import: '1'
status: public
supplementarymaterial: yes
title: Spectrum of Lévy–Khintchine random laplacian 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: 37
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'
das_tickbox: '0'
date_created: 2024-07-21T22:01:01Z
date_published: 2024-07-01T00:00:00Z
date_updated: 2026-10-16T08:32:45Z
day: '01'
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- '510'
department:
- _id: LaEr
doi: 10.1093/imrn/rnae062
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file_date_updated: 2024-07-22T06:40:19Z
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intvolume: ' 2024'
isi: 1
issue: '13'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 10189-10218
publication: International Mathematics Research Notices
publication_identifier:
eissn:
- 1687-0247
issn:
- 1073-7928
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: yes
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'
...