---
_id: '12232'
abstract:
- lang: eng
text: We derive a precise asymptotic formula for the density of the small singular
values of the real Ginibre matrix ensemble shifted by a complex parameter z as
the dimension tends to infinity. For z away from the real axis the formula coincides
with that for the complex Ginibre ensemble we derived earlier in Cipolloni et
al. (Prob Math Phys 1:101–146, 2020). On the level of the one-point function of
the low lying singular values we thus confirm the transition from real to complex
Ginibre ensembles as the shift parameter z becomes genuinely complex; the analogous
phenomenon has been well known for eigenvalues. We use the superbosonization formula
(Littelmann et al. in Comm Math Phys 283:343–395, 2008) in a regime where the
main contribution comes from a three dimensional saddle manifold.
acknowledgement: Open access funding provided by Swiss Federal Institute of Technology
Zurich. Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH
Zürich Foundation.
article_processing_charge: No
article_type: original
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: Cipolloni G, Erdös L, Schröder DJ. Density of small singular values of the
shifted real Ginibre ensemble. Annales Henri Poincaré. 2022;23(11):3981-4002.
doi:10.1007/s00023-022-01188-8
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Density of small singular
values of the shifted real Ginibre ensemble. Annales Henri Poincaré. Springer
Nature. https://doi.org/10.1007/s00023-022-01188-8
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Density of Small
Singular Values of the Shifted Real Ginibre Ensemble.” Annales Henri Poincaré.
Springer Nature, 2022. https://doi.org/10.1007/s00023-022-01188-8.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Density of small singular values
of the shifted real Ginibre ensemble,” Annales Henri Poincaré, vol. 23,
no. 11. Springer Nature, pp. 3981–4002, 2022.
ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Density of small singular values
of the shifted real Ginibre ensemble. Annales Henri Poincaré. 23(11), 3981–4002.
mla: Cipolloni, Giorgio, et al. “Density of Small Singular Values of the Shifted
Real Ginibre Ensemble.” Annales Henri Poincaré, vol. 23, no. 11, Springer
Nature, 2022, pp. 3981–4002, doi:10.1007/s00023-022-01188-8.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002.
date_created: 2023-01-16T09:50:26Z
date_published: 2022-11-01T00:00:00Z
date_updated: 2023-08-04T09:33:52Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00023-022-01188-8
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- '000796323500001'
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checksum: 5582f059feeb2f63e2eb68197a34d7dc
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creator: dernst
date_created: 2023-01-27T11:06:47Z
date_updated: 2023-01-27T11:06:47Z
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file_size: 1333638
relation: main_file
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intvolume: ' 23'
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keyword:
- Mathematical Physics
- Nuclear and High Energy Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '11'
oa: 1
oa_version: Published Version
page: 3981-4002
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: Density of small singular values of the shifted real Ginibre ensemble
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: 23
year: '2022'
...
---
_id: '12243'
abstract:
- lang: eng
text: 'We consider the eigenvalues of a large dimensional real or complex Ginibre
matrix in the region of the complex plane where their real parts reach their maximum
value. This maximum follows the Gumbel distribution and that these extreme eigenvalues
form a Poisson point process as the dimension asymptotically tends to infinity.
In the complex case, these facts have already been established by Bender [Probab.
Theory Relat. Fields 147, 241 (2010)] and in the real case by Akemann and Phillips
[J. Stat. Phys. 155, 421 (2014)] even for the more general elliptic ensemble with
a sophisticated saddle point analysis. The purpose of this article is to give
a very short direct proof in the Ginibre case with an effective error term. Moreover,
our estimates on the correlation kernel in this regime serve as a key input for
accurately locating [Formula: see text] for any large matrix X with i.i.d. entries
in the companion paper [G. Cipolloni et al., arXiv:2206.04448 (2022)]. '
acknowledgement: "The authors are grateful to G. Akemann for bringing Refs. 19 and
24–26 to their attention. Discussions with Guillaume Dubach on a preliminary version
of this project are acknowledged.\r\nL.E. and Y.X. were supported by the ERC Advanced
Grant “RMTBeyond” under Grant No. 101020331. D.S. was supported by Dr. Max Rössler,
the Walter Haefner Foundation, and the ETH Zürich Foundation."
article_number: '103303'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
- first_name: Yuanyuan
full_name: Xu, Yuanyuan
id: 7902bdb1-a2a4-11eb-a164-c9216f71aea3
last_name: Xu
orcid: 0000-0003-1559-1205
citation:
ama: Cipolloni G, Erdös L, Schröder DJ, Xu Y. Directional extremal statistics for
Ginibre eigenvalues. Journal of Mathematical Physics. 2022;63(10). doi:10.1063/5.0104290
apa: Cipolloni, G., Erdös, L., Schröder, D. J., & Xu, Y. (2022). Directional
extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics.
AIP Publishing. https://doi.org/10.1063/5.0104290
chicago: Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu.
“Directional Extremal Statistics for Ginibre Eigenvalues.” Journal of Mathematical
Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0104290.
ieee: G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “Directional extremal statistics
for Ginibre eigenvalues,” Journal of Mathematical Physics, vol. 63, no.
10. AIP Publishing, 2022.
ista: Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2022. Directional extremal statistics
for Ginibre eigenvalues. Journal of Mathematical Physics. 63(10), 103303.
mla: Cipolloni, Giorgio, et al. “Directional Extremal Statistics for Ginibre Eigenvalues.”
Journal of Mathematical Physics, vol. 63, no. 10, 103303, AIP Publishing,
2022, doi:10.1063/5.0104290.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, Journal of Mathematical Physics
63 (2022).
date_created: 2023-01-16T09:52:58Z
date_published: 2022-10-14T00:00:00Z
date_updated: 2025-04-14T07:57:18Z
day: '14'
ddc:
- '510'
- '530'
department:
- _id: LaEr
doi: 10.1063/5.0104290
ec_funded: 1
external_id:
arxiv:
- '2206.04443'
isi:
- '000869715800001'
file:
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checksum: 2db278ae5b07f345a7e3fec1f92b5c33
content_type: application/pdf
creator: dernst
date_created: 2023-01-30T08:01:10Z
date_updated: 2023-01-30T08:01:10Z
file_id: '12436'
file_name: 2022_JourMathPhysics_Cipolloni2.pdf
file_size: 7356807
relation: main_file
success: 1
file_date_updated: 2023-01-30T08:01:10Z
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intvolume: ' 63'
isi: 1
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keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
project:
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call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Journal of Mathematical Physics
publication_identifier:
eissn:
- 1089-7658
issn:
- 0022-2488
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Directional extremal statistics for Ginibre eigenvalues
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 63
year: '2022'
...
---
_id: '12290'
abstract:
- lang: eng
text: We prove local laws, i.e. optimal concentration estimates for arbitrary products
of resolvents of a Wigner random matrix with deterministic matrices in between.
We find that the size of such products heavily depends on whether some of the
deterministic matrices are traceless. Our estimates correctly account for this
dependence and they hold optimally down to the smallest possible spectral scale.
acknowledgement: L. Erdős was supported by ERC Advanced Grant “RMTBeyond” No. 101020331.
D. Schröder was supported by Dr. Max Rössler, the Walter Haefner Foundation and
the ETH Zürich Foundation.
article_processing_charge: No
article_type: original
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: Cipolloni G, Erdös L, Schröder DJ. Optimal multi-resolvent local laws for Wigner
matrices. Electronic Journal of Probability. 2022;27:1-38. doi:10.1214/22-ejp838
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Optimal multi-resolvent
local laws for Wigner matrices. Electronic Journal of Probability. Institute
of Mathematical Statistics. https://doi.org/10.1214/22-ejp838
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Multi-Resolvent
Local Laws for Wigner Matrices.” Electronic Journal of Probability. Institute
of Mathematical Statistics, 2022. https://doi.org/10.1214/22-ejp838.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal multi-resolvent local
laws for Wigner matrices,” Electronic Journal of Probability, vol. 27.
Institute of Mathematical Statistics, pp. 1–38, 2022.
ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws
for Wigner matrices. Electronic Journal of Probability. 27, 1–38.
mla: Cipolloni, Giorgio, et al. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.”
Electronic Journal of Probability, vol. 27, Institute of Mathematical Statistics,
2022, pp. 1–38, doi:10.1214/22-ejp838.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability
27 (2022) 1–38.
corr_author: '1'
date_created: 2023-01-16T10:04:38Z
date_published: 2022-09-12T00:00:00Z
date_updated: 2025-04-14T07:57:19Z
day: '12'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1214/22-ejp838
ec_funded: 1
external_id:
isi:
- '000910863700003'
file:
- access_level: open_access
checksum: bb647b48fbdb59361210e425c220cdcb
content_type: application/pdf
creator: dernst
date_created: 2023-01-30T11:59:21Z
date_updated: 2023-01-30T11:59:21Z
file_id: '12464'
file_name: 2022_ElecJournProbability_Cipolloni.pdf
file_size: 502149
relation: main_file
success: 1
file_date_updated: 2023-01-30T11:59:21Z
has_accepted_license: '1'
intvolume: ' 27'
isi: 1
keyword:
- Statistics
- Probability and Uncertainty
- Statistics and Probability
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 1-38
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Electronic Journal of Probability
publication_identifier:
eissn:
- 1083-6489
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal multi-resolvent local laws for Wigner matrices
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: 27
year: '2022'
...
---
_id: '10600'
abstract:
- lang: eng
text: We show that recent results on adiabatic theory for interacting gapped many-body
systems on finite lattices remain valid in the thermodynamic limit. More precisely,
we prove a generalized super-adiabatic theorem for the automorphism group describing
the infinite volume dynamics on the quasi-local algebra of observables. The key
assumption is the existence of a sequence of gapped finite volume Hamiltonians,
which generates the same infinite volume dynamics in the thermodynamic limit.
Our adiabatic theorem also holds for certain perturbations of gapped ground states
that close the spectral gap (so it is also an adiabatic theorem for resonances
and, in this sense, “generalized”), and it provides an adiabatic approximation
to all orders in the adiabatic parameter (a property often called “super-adiabatic”).
In addition to the existing results for finite lattices, we also perform a resummation
of the adiabatic expansion and allow for observables that are not strictly local.
Finally, as an application, we prove the validity of linear and higher order response
theory for our class of perturbations for infinite systems. While we consider
the result and its proof as new and interesting in itself, we also lay the foundation
for the proof of an adiabatic theorem for systems with a gap only in the bulk,
which will be presented in a follow-up article.
acknowledgement: J.H. acknowledges partial financial support from ERC Advanced Grant
“RMTBeyond” No. 101020331.
article_number: '011901'
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
citation:
ama: 'Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems
with a uniform gap. Journal of Mathematical Physics. 2022;63(1). doi:10.1063/5.0051632'
apa: 'Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic
limit: Systems with a uniform gap. Journal of Mathematical Physics. AIP
Publishing. https://doi.org/10.1063/5.0051632'
chicago: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic
Limit: Systems with a Uniform Gap.” Journal of Mathematical Physics. AIP
Publishing, 2022. https://doi.org/10.1063/5.0051632.'
ieee: 'S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit:
Systems with a uniform gap,” Journal of Mathematical Physics, vol. 63,
no. 1. AIP Publishing, 2022.'
ista: 'Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit:
Systems with a uniform gap. Journal of Mathematical Physics. 63(1), 011901.'
mla: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic
Limit: Systems with a Uniform Gap.” Journal of Mathematical Physics, vol.
63, no. 1, 011901, AIP Publishing, 2022, doi:10.1063/5.0051632.'
short: S.J. Henheik, S. Teufel, Journal of Mathematical Physics 63 (2022).
date_created: 2022-01-03T12:19:48Z
date_published: 2022-01-03T00:00:00Z
date_updated: 2025-04-14T07:57:17Z
day: '03'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1063/5.0051632
ec_funded: 1
external_id:
arxiv:
- '2012.15238'
isi:
- '000739446000009'
intvolume: ' 63'
isi: 1
issue: '1'
keyword:
- mathematical physics
- statistical and nonlinear physics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2012.15238
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: Journal of Mathematical Physics
publication_identifier:
eissn:
- 1089-7658
issn:
- 0022-2488
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap'
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 63
year: '2022'
...
---
_id: '10643'
abstract:
- lang: eng
text: "We prove a generalised super-adiabatic theorem for extended fermionic systems
assuming a spectral gap only in the bulk. More precisely, we assume that the infinite
system has a unique ground state and that the corresponding Gelfand–Naimark–Segal
Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that
a similar adiabatic theorem also holds in the bulk of finite systems up to errors
that vanish faster than any inverse power of the system size, although the corresponding
finite-volume Hamiltonians need not have a spectral gap.\r\n\r\n"
acknowledgement: J.H. acknowledges partial financial support by the ERC Advanced Grant
‘RMTBeyond’ No. 101020331. Support for publication costs from the Deutsche Forschungsgemeinschaft
and the Open Access Publishing Fund of the University of Tübingen is gratefully
acknowledged.
article_number: e4
article_processing_charge: Yes
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
citation:
ama: 'Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems
with a gap in the bulk. Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2021.80'
apa: 'Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic
limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. Cambridge
University Press. https://doi.org/10.1017/fms.2021.80'
chicago: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic
Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma. Cambridge
University Press, 2022. https://doi.org/10.1017/fms.2021.80.'
ieee: 'S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit:
Systems with a gap in the bulk,” Forum of Mathematics, Sigma, vol. 10.
Cambridge University Press, 2022.'
ista: 'Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit:
Systems with a gap in the bulk. Forum of Mathematics, Sigma. 10, e4.'
mla: 'Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic
Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma, vol.
10, e4, Cambridge University Press, 2022, doi:10.1017/fms.2021.80.'
short: S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022).
corr_author: '1'
date_created: 2022-01-18T16:18:51Z
date_published: 2022-01-18T00:00:00Z
date_updated: 2025-04-14T07:57:17Z
day: '18'
ddc:
- '510'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1017/fms.2021.80
ec_funded: 1
external_id:
arxiv:
- '2012.15239'
isi:
- '000743615000001'
file:
- access_level: open_access
checksum: 87592a755adcef22ea590a99dc728dd3
content_type: application/pdf
creator: cchlebak
date_created: 2022-01-19T09:27:43Z
date_updated: 2022-01-19T09:27:43Z
file_id: '10646'
file_name: 2022_ForumMathSigma_Henheik.pdf
file_size: 705323
relation: main_file
success: 1
file_date_updated: 2022-01-19T09:27:43Z
has_accepted_license: '1'
intvolume: ' 10'
isi: 1
keyword:
- computational mathematics
- discrete mathematics and combinatorics
- geometry and topology
- mathematical physics
- statistics and probability
- algebra and number theory
- theoretical computer science
- analysis
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Forum of Mathematics, Sigma
publication_identifier:
eissn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 10
year: '2022'
...
---
_id: '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:
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- '2102.09975'
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- '000781239100004'
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publication: Journal of Functional Analysis
publication_identifier:
eissn:
- 1096-0783
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title: Thermalisation for Wigner matrices
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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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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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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'
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- geometry and topology
- mathematical physics
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- iso: eng
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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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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:
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- '2208.12220'
isi:
- '000905776200001'
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month: '12'
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grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
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title: On adiabatic theory for extended fermionic lattice systems
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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
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doi: 10.1007/s11005-021-01494-y
ec_funded: 1
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arxiv:
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pmid:
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call_identifier: H2020
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name: Random matrices beyond Wigner-Dyson-Mehta
publication: Letters in Mathematical Physics
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- 1573-0530
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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
file_size: 419563
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success: 1
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
status: public
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
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intvolume: ' 26'
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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'
...