---
_id: '15025'
abstract:
- lang: eng
text: We consider quadratic forms of deterministic matrices A evaluated at the random
eigenvectors of a large N×N GOE or GUE matrix, or equivalently evaluated at the
columns of a Haar-orthogonal or Haar-unitary random matrix. We prove that, as
long as the deterministic matrix has rank much smaller than √N, the distributions
of the extrema of these quadratic forms are asymptotically the same as if the
eigenvectors were independent Gaussians. This reduces the problem to Gaussian
computations, which we carry out in several cases to illustrate our result, finding
Gumbel or Weibull limiting distributions depending on the signature of A. Our
result also naturally applies to the eigenvectors of any invariant ensemble.
acknowledgement: The first author was supported by the ERC Advanced Grant “RMTBeyond”
No. 101020331. The second author was supported by Fulbright Austria and the Austrian
Marshall Plan Foundation.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Benjamin
full_name: McKenna, Benjamin
id: b0cc634c-d549-11ee-96c8-87338c7ad808
last_name: McKenna
orcid: 0000-0003-2625-495X
citation:
ama: Erdös L, McKenna B. Extremal statistics of quadratic forms of GOE/GUE eigenvectors.
Annals of Applied Probability. 2024;34(1B):1623-1662. doi:10.1214/23-AAP2000
apa: Erdös, L., & McKenna, B. (2024). Extremal statistics of quadratic forms
of GOE/GUE eigenvectors. Annals of Applied Probability. Institute of Mathematical
Statistics. https://doi.org/10.1214/23-AAP2000
chicago: Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic
Forms of GOE/GUE Eigenvectors.” Annals of Applied Probability. Institute
of Mathematical Statistics, 2024. https://doi.org/10.1214/23-AAP2000.
ieee: L. Erdös and B. McKenna, “Extremal statistics of quadratic forms of GOE/GUE
eigenvectors,” Annals of Applied Probability, vol. 34, no. 1B. Institute
of Mathematical Statistics, pp. 1623–1662, 2024.
ista: Erdös L, McKenna B. 2024. Extremal statistics of quadratic forms of GOE/GUE
eigenvectors. Annals of Applied Probability. 34(1B), 1623–1662.
mla: Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms
of GOE/GUE Eigenvectors.” Annals of Applied Probability, vol. 34, no. 1B,
Institute of Mathematical Statistics, 2024, pp. 1623–62, doi:10.1214/23-AAP2000.
short: L. Erdös, B. McKenna, Annals of Applied Probability 34 (2024) 1623–1662.
date_created: 2024-02-25T23:00:56Z
date_published: 2024-02-01T00:00:00Z
date_updated: 2024-02-27T08:29:05Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/23-AAP2000
ec_funded: 1
external_id:
arxiv:
- '2208.12206'
intvolume: ' 34'
issue: 1B
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2208.12206
month: '02'
oa: 1
oa_version: Preprint
page: 1623-1662
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Annals of Applied Probability
publication_identifier:
issn:
- 1050-5164
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Extremal statistics of quadratic forms of GOE/GUE eigenvectors
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 34
year: '2024'
...
---
_id: '14343'
abstract:
- lang: eng
text: The total energy of an eigenstate in a composite quantum system tends to be
distributed equally among its constituents. We identify the quantum fluctuation
around this equipartition principle in the simplest disordered quantum system
consisting of linear combinations of Wigner matrices. As our main ingredient,
we prove the Eigenstate Thermalisation Hypothesis and Gaussian fluctuation for
general quadratic forms of the bulk eigenvectors of Wigner matrices with an arbitrary
deformation.
acknowledgement: "G.C. and L.E. gratefully acknowledge many discussions with Dominik
Schröder at the preliminary stage of this project, especially his essential contribution
to identify the correct generalisation of traceless observables to the deformed
Wigner ensembles.\r\nL.E. and J.H. acknowledges support by ERC Advanced Grant ‘RMTBeyond’
No. 101020331."
article_number: e74
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- first_name: Oleksii
full_name: Kolupaiev, Oleksii
id: 149b70d4-896a-11ed-bdf8-8c63fd44ca61
last_name: Kolupaiev
citation:
ama: Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Gaussian fluctuations in the
equipartition principle for Wigner matrices. Forum of Mathematics, Sigma.
2023;11. doi:10.1017/fms.2023.70
apa: Cipolloni, G., Erdös, L., Henheik, S. J., & Kolupaiev, O. (2023). Gaussian
fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics,
Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2023.70
chicago: Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev.
“Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” Forum
of Mathematics, Sigma. Cambridge University Press, 2023. https://doi.org/10.1017/fms.2023.70.
ieee: G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Gaussian fluctuations
in the equipartition principle for Wigner matrices,” Forum of Mathematics,
Sigma, vol. 11. Cambridge University Press, 2023.
ista: Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2023. Gaussian fluctuations
in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma.
11, e74.
mla: Cipolloni, Giorgio, et al. “Gaussian Fluctuations in the Equipartition Principle
for Wigner Matrices.” Forum of Mathematics, Sigma, vol. 11, e74, Cambridge
University Press, 2023, doi:10.1017/fms.2023.70.
short: G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Forum of Mathematics,
Sigma 11 (2023).
date_created: 2023-09-17T22:01:09Z
date_published: 2023-08-23T00:00:00Z
date_updated: 2023-12-13T12:24:23Z
day: '23'
ddc:
- '510'
department:
- _id: LaEr
- _id: GradSch
doi: 10.1017/fms.2023.70
ec_funded: 1
external_id:
arxiv:
- '2301.05181'
isi:
- '001051980200001'
file:
- access_level: open_access
checksum: eb747420e6a88a7796fa934151957676
content_type: application/pdf
creator: dernst
date_created: 2023-09-20T11:09:35Z
date_updated: 2023-09-20T11:09:35Z
file_id: '14352'
file_name: 2023_ForumMathematics_Cipolloni.pdf
file_size: 852652
relation: main_file
success: 1
file_date_updated: 2023-09-20T11:09:35Z
has_accepted_license: '1'
intvolume: ' 11'
isi: 1
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Forum of Mathematics, Sigma
publication_identifier:
eissn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Gaussian fluctuations in the equipartition principle for Wigner matrices
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 11
year: '2023'
...
---
_id: '14421'
abstract:
- lang: eng
text: Only recently has it been possible to construct a self-adjoint Hamiltonian
that involves the creation of Dirac particles at a point source in 3d space. Its
definition makes use of an interior-boundary condition. Here, we develop for this
Hamiltonian a corresponding theory of the Bohmian configuration. That is, we (non-rigorously)
construct a Markov jump process $(Q_t)_{t\in\mathbb{R}}$ in the configuration
space of a variable number of particles that is $|\psi_t|^2$-distributed at every
time t and follows Bohmian trajectories between the jumps. The jumps correspond
to particle creation or annihilation events and occur either to or from a configuration
with a particle located at the source. The process is the natural analog of Bell's
jump process, and a central piece in its construction is the determination of
the rate of particle creation. The construction requires an analysis of the asymptotic
behavior of the Bohmian trajectories near the source. We find that the particle
reaches the source with radial speed 0, but orbits around the source infinitely
many times in finite time before absorption (or after emission).
acknowledgement: J H gratefully acknowledges partial financial support by the ERC
Advanced Grant 'RMTBeyond' No. 101020331.
article_number: '445201'
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
- first_name: Roderich
full_name: Tumulka, Roderich
last_name: Tumulka
citation:
ama: 'Henheik SJ, Tumulka R. Creation rate of Dirac particles at a point source.
Journal of Physics A: Mathematical and Theoretical. 2023;56(44). doi:10.1088/1751-8121/acfe62'
apa: 'Henheik, S. J., & Tumulka, R. (2023). Creation rate of Dirac particles
at a point source. Journal of Physics A: Mathematical and Theoretical.
IOP Publishing. https://doi.org/10.1088/1751-8121/acfe62'
chicago: 'Henheik, Sven Joscha, and Roderich Tumulka. “Creation Rate of Dirac Particles
at a Point Source.” Journal of Physics A: Mathematical and Theoretical.
IOP Publishing, 2023. https://doi.org/10.1088/1751-8121/acfe62.'
ieee: 'S. J. Henheik and R. Tumulka, “Creation rate of Dirac particles at a point
source,” Journal of Physics A: Mathematical and Theoretical, vol. 56, no.
44. IOP Publishing, 2023.'
ista: 'Henheik SJ, Tumulka R. 2023. Creation rate of Dirac particles at a point
source. Journal of Physics A: Mathematical and Theoretical. 56(44), 445201.'
mla: 'Henheik, Sven Joscha, and Roderich Tumulka. “Creation Rate of Dirac Particles
at a Point Source.” Journal of Physics A: Mathematical and Theoretical,
vol. 56, no. 44, 445201, IOP Publishing, 2023, doi:10.1088/1751-8121/acfe62.'
short: 'S.J. Henheik, R. Tumulka, Journal of Physics A: Mathematical and Theoretical
56 (2023).'
date_created: 2023-10-12T12:42:53Z
date_published: 2023-10-11T00:00:00Z
date_updated: 2023-12-13T13:01:25Z
day: '11'
ddc:
- '510'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1088/1751-8121/acfe62
ec_funded: 1
external_id:
arxiv:
- '2211.16606'
isi:
- '001080908000001'
file:
- access_level: open_access
checksum: 5b68de147dd4c608b71a6e0e844d2ce9
content_type: application/pdf
creator: dernst
date_created: 2023-10-16T07:07:24Z
date_updated: 2023-10-16T07:07:24Z
file_id: '14429'
file_name: 2023_JourPhysics_Henheik.pdf
file_size: 721399
relation: main_file
success: 1
file_date_updated: 2023-10-16T07:07:24Z
has_accepted_license: '1'
intvolume: ' 56'
isi: 1
issue: '44'
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: 'Journal of Physics A: Mathematical and Theoretical'
publication_identifier:
eissn:
- 1751-8121
issn:
- 1751-8113
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Creation rate of Dirac particles at a point source
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: 56
year: '2023'
...
---
_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. 2023. doi:10.1142/s0129055x2360005x
apa: Henheik, S. J., Lauritsen, A. B., & Roos, B. (2023). 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, 2023. 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. World Scientific Publishing,
2023.
ista: Henheik SJ, Lauritsen AB, Roos B. 2023. Universality in low-dimensional BCS
theory. Reviews in Mathematical Physics., 2360005.
mla: Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.”
Reviews in Mathematical Physics, 2360005, World Scientific Publishing,
2023, doi:10.1142/s0129055x2360005x.
short: S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics (2023).
date_created: 2023-11-15T23:48:14Z
date_published: 2023-10-31T00:00:00Z
date_updated: 2023-11-20T10:04:38Z
day: '31'
department:
- _id: GradSch
- _id: LaEr
- _id: RoSe
doi: 10.1142/s0129055x2360005x
ec_funded: 1
external_id:
arxiv:
- '2301.05621'
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1142/S0129055X2360005X
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: epub_ahead
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Universality in low-dimensional BCS theory
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '14667'
abstract:
- lang: eng
text: 'For large dimensional non-Hermitian random matrices X with real or complex
independent, identically distributed, centered entries, we consider the fluctuations
of f (X) as a matrix where f is an analytic function around the spectrum of X.
We prove that for a generic bounded square matrix A, the quantity Tr f (X)A exhibits
Gaussian fluctuations as the matrix size grows to infinity, which consists of
two independent modes corresponding to the tracial and traceless parts of A. We
find a new formula for the variance of the traceless part that involves the Frobenius
norm of A and the L2-norm of f on the boundary of the limiting spectrum. '
- lang: fre
text: On étudie les fluctuations de f (X), où X est une matrice aléatoire non-hermitienne
de grande taille à coefficients i.i.d. (réels ou complexes), et f une fonction
analytique sur un domaine qui contient le spectre de X. On prouve que, pour une
matrice carrée générique et bornée A, les fluctuations de la quantité tr f (X)A
sont asymptotiquement gaussiennes et comportent deux modes indépendants, correspondant
aux composantes traciale et de trace nulle de A. Une nouvelle formule est établie
pour la variance de la composante de trace nulle, qui fait intervenir la norme
de Frobenius de A et la norme L2 de f sur la frontière du spectre limite.
acknowledgement: "The first author was partially supported by ERC Advanced Grant “RMTBeyond”
No. 101020331. The second author was supported by ERC Advanced Grant “RMTBeyond”
No. 101020331.\r\nThe authors are grateful to the anonymous referees and associated
editor for carefully reading this paper and providing helpful comments that improved
the quality of the article. Also the authors would like to thank Peter Forrester
for pointing out the reference [12] that was absent in the previous version of the
manuscript."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Hong Chang
full_name: Ji, Hong Chang
id: dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d
last_name: Ji
citation:
ama: Erdös L, Ji HC. Functional CLT for non-Hermitian random matrices. Annales
de l’institut Henri Poincare (B) Probability and Statistics. 2023;59(4):2083-2105.
doi:10.1214/22-AIHP1304
apa: Erdös, L., & Ji, H. C. (2023). Functional CLT for non-Hermitian random
matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics.
Institute of Mathematical Statistics. https://doi.org/10.1214/22-AIHP1304
chicago: Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random
Matrices.” Annales de l’institut Henri Poincare (B) Probability and Statistics.
Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/22-AIHP1304.
ieee: L. Erdös and H. C. Ji, “Functional CLT for non-Hermitian random matrices,”
Annales de l’institut Henri Poincare (B) Probability and Statistics, vol.
59, no. 4. Institute of Mathematical Statistics, pp. 2083–2105, 2023.
ista: Erdös L, Ji HC. 2023. Functional CLT for non-Hermitian random matrices. Annales
de l’institut Henri Poincare (B) Probability and Statistics. 59(4), 2083–2105.
mla: Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random
Matrices.” Annales de l’institut Henri Poincare (B) Probability and Statistics,
vol. 59, no. 4, Institute of Mathematical Statistics, 2023, pp. 2083–105, doi:10.1214/22-AIHP1304.
short: L. Erdös, H.C. Ji, Annales de l’institut Henri Poincare (B) Probability and
Statistics 59 (2023) 2083–2105.
date_created: 2023-12-10T23:01:00Z
date_published: 2023-11-01T00:00:00Z
date_updated: 2023-12-11T12:36:56Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/22-AIHP1304
ec_funded: 1
external_id:
arxiv:
- '2112.11382'
intvolume: ' 59'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2112.11382
month: '11'
oa: 1
oa_version: Preprint
page: 2083-2105
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Annales de l'institut Henri Poincare (B) Probability and Statistics
publication_identifier:
issn:
- 0246-0203
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Functional CLT for non-Hermitian random matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 59
year: '2023'
...
---
_id: '14750'
abstract:
- lang: eng
text: "Consider the random matrix model A1/2UBU∗A1/2, where A and B are two N ×
N deterministic matrices and U is either an N × N Haar unitary or orthogonal random
matrix. It is well known that on the macroscopic scale (Invent. Math. 104 (1991)
201–220), the limiting empirical spectral distribution (ESD) of the above model
is given by the free multiplicative convolution\r\nof the limiting ESDs of A and
B, denoted as μα \x02 μβ, where μα and μβ are the limiting ESDs of A and B, respectively.
In this paper, we study the asymptotic microscopic behavior of the edge eigenvalues
and eigenvectors statistics. We prove that both the density of μA \x02μB, where
μA and μB are the ESDs of A and B, respectively and the associated subordination
functions\r\nhave a regular behavior near the edges. Moreover, we establish the
local laws near the edges on the optimal scale. In particular, we prove that the
entries of the resolvent are close to some functionals depending only on the eigenvalues
of A, B and the subordination functions with optimal convergence rates. Our proofs
and calculations are based on the techniques developed for the additive model
A+UBU∗ in (J. Funct. Anal. 271 (2016) 672–719; Comm. Math.\r\nPhys. 349 (2017)
947–990; Adv. Math. 319 (2017) 251–291; J. Funct. Anal. 279 (2020) 108639), and
our results can be regarded as the counterparts of (J. Funct. Anal. 279 (2020)
108639) for the multiplicative model. "
acknowledgement: "The first author is partially supported by NSF Grant DMS-2113489
and grateful for the AMS-SIMONS travel grant (2020–2023). The second author is supported
by the ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nThe authors would like to
thank the Editor, Associate Editor and an anonymous referee for their many critical
suggestions which have significantly improved the paper. We also want to thank Zhigang
Bao and Ji Oon Lee for many helpful discussions and comments."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Xiucai
full_name: Ding, Xiucai
last_name: Ding
- first_name: Hong Chang
full_name: Ji, Hong Chang
id: dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d
last_name: Ji
citation:
ama: Ding X, Ji HC. Local laws for multiplication of random matrices. The Annals
of Applied Probability. 2023;33(4):2981-3009. doi:10.1214/22-aap1882
apa: Ding, X., & Ji, H. C. (2023). Local laws for multiplication of random matrices.
The Annals of Applied Probability. Institute of Mathematical Statistics.
https://doi.org/10.1214/22-aap1882
chicago: Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random
Matrices.” The Annals of Applied Probability. Institute of Mathematical
Statistics, 2023. https://doi.org/10.1214/22-aap1882.
ieee: X. Ding and H. C. Ji, “Local laws for multiplication of random matrices,”
The Annals of Applied Probability, vol. 33, no. 4. Institute of Mathematical
Statistics, pp. 2981–3009, 2023.
ista: Ding X, Ji HC. 2023. Local laws for multiplication of random matrices. The
Annals of Applied Probability. 33(4), 2981–3009.
mla: Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random Matrices.”
The Annals of Applied Probability, vol. 33, no. 4, Institute of Mathematical
Statistics, 2023, pp. 2981–3009, doi:10.1214/22-aap1882.
short: X. Ding, H.C. Ji, The Annals of Applied Probability 33 (2023) 2981–3009.
date_created: 2024-01-08T13:03:18Z
date_published: 2023-08-01T00:00:00Z
date_updated: 2024-01-09T08:16:41Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/22-aap1882
ec_funded: 1
external_id:
arxiv:
- '2010.16083'
intvolume: ' 33'
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.2010.16083
month: '08'
oa: 1
oa_version: Preprint
page: 2981-3009
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: The Annals of Applied Probability
publication_identifier:
issn:
- 1050-5164
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local laws for multiplication of random matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 33
year: '2023'
...
---
_id: '14775'
abstract:
- lang: eng
text: We establish a quantitative version of the Tracy–Widom law for the largest
eigenvalue of high-dimensional sample covariance matrices. To be precise, we show
that the fluctuations of the largest eigenvalue of a sample covariance matrix
X∗X converge to its Tracy–Widom limit at a rate nearly N−1/3, where X is an M×N
random matrix whose entries are independent real or complex random variables,
assuming that both M and N tend to infinity at a constant rate. This result improves
the previous estimate N−2/9 obtained by Wang (2019). Our proof relies on a Green
function comparison method (Adv. Math. 229 (2012) 1435–1515) using iterative cumulant
expansions, the local laws for the Green function and asymptotic properties of
the correlation kernel of the white Wishart ensemble.
acknowledgement: K. Schnelli was supported by the Swedish Research Council Grants
VR-2017-05195, and the Knut and Alice Wallenberg Foundation. Y. Xu was 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 sample covariance matrices. The Annals of Applied Probability.
2023;33(1):677-725. doi:10.1214/22-aap1826
apa: Schnelli, K., & Xu, Y. (2023). Convergence rate to the Tracy–Widom laws
for the largest eigenvalue of sample covariance matrices. The Annals of Applied
Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/22-aap1826
chicago: Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom
Laws for the Largest Eigenvalue of Sample Covariance Matrices.” The Annals
of Applied Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/22-aap1826.
ieee: K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest
eigenvalue of sample covariance matrices,” The Annals of Applied Probability,
vol. 33, no. 1. Institute of Mathematical Statistics, pp. 677–725, 2023.
ista: Schnelli K, Xu Y. 2023. Convergence rate to the Tracy–Widom laws for the largest
eigenvalue of sample covariance matrices. The Annals of Applied Probability. 33(1),
677–725.
mla: Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws
for the Largest Eigenvalue of Sample Covariance Matrices.” The Annals of Applied
Probability, vol. 33, no. 1, Institute of Mathematical Statistics, 2023, pp.
677–725, doi:10.1214/22-aap1826.
short: K. Schnelli, Y. Xu, The Annals of Applied Probability 33 (2023) 677–725.
date_created: 2024-01-10T09:23:31Z
date_published: 2023-02-01T00:00:00Z
date_updated: 2024-01-10T13:31:46Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/22-aap1826
ec_funded: 1
external_id:
arxiv:
- '2108.02728'
isi:
- '000946432400021'
intvolume: ' 33'
isi: 1
issue: '1'
keyword:
- Statistics
- Probability and Uncertainty
- Statistics and Probability
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2108.02728
month: '02'
oa: 1
oa_version: Preprint
page: 677-725
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: The Annals of Applied Probability
publication_identifier:
issn:
- 1050-5164
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample
covariance matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 33
year: '2023'
...
---
_id: '14780'
abstract:
- lang: eng
text: In this paper, we study the eigenvalues and eigenvectors of the spiked invariant
multiplicative models when the randomness is from Haar matrices. We establish
the limits of the outlier eigenvalues λˆi and the generalized components (⟨v,uˆi⟩
for any deterministic vector v) of the outlier eigenvectors uˆi with optimal convergence
rates. Moreover, we prove that the non-outlier eigenvalues stick with those of
the unspiked matrices and the non-outlier eigenvectors are delocalized. The results
also hold near the so-called BBP transition and for degenerate spikes. On one
hand, our results can be regarded as a refinement of the counterparts of [12]
under additional regularity conditions. On the other hand, they can be viewed
as an analog of [34] by replacing the random matrix with i.i.d. entries with Haar
random matrix.
acknowledgement: The authors would like to thank the editor, the associated editor
and two anonymous referees for their many critical suggestions which have significantly
improved the paper. The authors are also grateful to Zhigang Bao and Ji Oon Lee
for many helpful discussions. The first author also wants to thank Hari Bercovici
for many useful comments. The first author is partially supported by National Science
Foundation DMS-2113489 and the second author is supported by ERC Advanced Grant
“RMTBeyond” No. 101020331.
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Xiucai
full_name: Ding, Xiucai
last_name: Ding
- first_name: Hong Chang
full_name: Ji, Hong Chang
id: dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d
last_name: Ji
citation:
ama: Ding X, Ji HC. Spiked multiplicative random matrices and principal components.
Stochastic Processes and their Applications. 2023;163:25-60. doi:10.1016/j.spa.2023.05.009
apa: Ding, X., & Ji, H. C. (2023). Spiked multiplicative random matrices and
principal components. Stochastic Processes and Their Applications. Elsevier.
https://doi.org/10.1016/j.spa.2023.05.009
chicago: Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices
and Principal Components.” Stochastic Processes and Their Applications.
Elsevier, 2023. https://doi.org/10.1016/j.spa.2023.05.009.
ieee: X. Ding and H. C. Ji, “Spiked multiplicative random matrices and principal
components,” Stochastic Processes and their Applications, vol. 163. Elsevier,
pp. 25–60, 2023.
ista: Ding X, Ji HC. 2023. Spiked multiplicative random matrices and principal components.
Stochastic Processes and their Applications. 163, 25–60.
mla: Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and
Principal Components.” Stochastic Processes and Their Applications, vol.
163, Elsevier, 2023, pp. 25–60, doi:10.1016/j.spa.2023.05.009.
short: X. Ding, H.C. Ji, Stochastic Processes and Their Applications 163 (2023)
25–60.
date_created: 2024-01-10T09:29:25Z
date_published: 2023-09-01T00:00:00Z
date_updated: 2024-01-16T08:49:51Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1016/j.spa.2023.05.009
ec_funded: 1
external_id:
arxiv:
- '2302.13502'
isi:
- '001113615900001'
file:
- access_level: open_access
checksum: 46a708b0cd5569a73d0f3d6c3e0a44dc
content_type: application/pdf
creator: dernst
date_created: 2024-01-16T08:47:31Z
date_updated: 2024-01-16T08:47:31Z
file_id: '14806'
file_name: 2023_StochasticProcAppl_Ding.pdf
file_size: 1870349
relation: main_file
success: 1
file_date_updated: 2024-01-16T08:47:31Z
has_accepted_license: '1'
intvolume: ' 163'
isi: 1
keyword:
- Applied Mathematics
- Modeling and Simulation
- Statistics and Probability
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 25-60
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Stochastic Processes and their Applications
publication_identifier:
eissn:
- 1879-209X
issn:
- 0304-4149
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: Spiked multiplicative random matrices and principal components
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: 163
year: '2023'
...
---
_id: '14849'
abstract:
- lang: eng
text: We establish a precise three-term asymptotic expansion, with an optimal estimate
of the error term, for the rightmost eigenvalue of an n×n random matrix with independent
identically distributed complex entries as n tends to infinity. All terms in the
expansion are universal.
acknowledgement: "The second and the fourth author were supported by the ERC Advanced
Grant\r\n“RMTBeyond” No. 101020331. The third author was supported by Dr. Max Rössler,
the\r\nWalter Haefner Foundation and the ETH Zürich Foundation."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
- first_name: Yuanyuan
full_name: Xu, Yuanyuan
last_name: Xu
citation:
ama: Cipolloni G, Erdös L, Schröder DJ, Xu Y. On the rightmost eigenvalue of non-Hermitian
random matrices. The Annals of Probability. 2023;51(6):2192-2242. doi:10.1214/23-aop1643
apa: Cipolloni, G., Erdös, L., Schröder, D. J., & Xu, Y. (2023). On the rightmost
eigenvalue of non-Hermitian random matrices. The Annals of Probability.
Institute of Mathematical Statistics. https://doi.org/10.1214/23-aop1643
chicago: Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu.
“On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” The Annals
of Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/23-aop1643.
ieee: G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “On the rightmost eigenvalue
of non-Hermitian random matrices,” The Annals of Probability, vol. 51,
no. 6. Institute of Mathematical Statistics, pp. 2192–2242, 2023.
ista: Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2023. On the rightmost eigenvalue
of non-Hermitian random matrices. The Annals of Probability. 51(6), 2192–2242.
mla: Cipolloni, Giorgio, et al. “On the Rightmost Eigenvalue of Non-Hermitian Random
Matrices.” The Annals of Probability, vol. 51, no. 6, Institute of Mathematical
Statistics, 2023, pp. 2192–242, doi:10.1214/23-aop1643.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, The Annals of Probability 51
(2023) 2192–2242.
date_created: 2024-01-22T08:08:41Z
date_published: 2023-11-01T00:00:00Z
date_updated: 2024-01-23T10:56:30Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/23-aop1643
ec_funded: 1
external_id:
arxiv:
- '2206.04448'
intvolume: ' 51'
issue: '6'
keyword:
- Statistics
- Probability and Uncertainty
- Statistics and Probability
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2206.04448
month: '11'
oa: 1
oa_version: Preprint
page: 2192-2242
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: The Annals of Probability
publication_identifier:
issn:
- 0091-1798
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
status: public
title: On the rightmost eigenvalue of non-Hermitian random matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 51
year: '2023'
...
---
_id: '13317'
abstract:
- lang: eng
text: We prove the Eigenstate Thermalisation Hypothesis (ETH) for local observables
in a typical translation invariant system of quantum spins with L-body interactions,
where L is the number of spins. This mathematically verifies the observation first
made by Santos and Rigol (Phys Rev E 82(3):031130, 2010, https://doi.org/10.1103/PhysRevE.82.031130)
that the ETH may hold for systems with additional translational symmetries for
a naturally restricted class of observables. We also present numerical support
for the same phenomenon for Hamiltonians with local interaction.
acknowledgement: "LE, JH, and VR were supported by ERC Advanced Grant “RMTBeyond”
No. 101020331. SS was supported by KAKENHI Grant Number JP22J14935 from the Japan
Society for the Promotion of Science (JSPS) and Forefront Physics and Mathematics
Program to Drive Transformation (FoPM), a World-leading Innovative Graduate Study
(WINGS) Program, the University of Tokyo.\r\nOpen access funding provided by The
University of Tokyo."
article_number: '128'
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Shoki
full_name: Sugimoto, Shoki
last_name: Sugimoto
- first_name: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- first_name: Volodymyr
full_name: Riabov, Volodymyr
id: 1949f904-edfb-11eb-afb5-e2dfddabb93b
last_name: Riabov
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
citation:
ama: Sugimoto S, Henheik SJ, Riabov V, Erdös L. Eigenstate thermalisation hypothesis
for translation invariant spin systems. Journal of Statistical Physics.
2023;190(7). doi:10.1007/s10955-023-03132-4
apa: Sugimoto, S., Henheik, S. J., Riabov, V., & Erdös, L. (2023). Eigenstate
thermalisation hypothesis for translation invariant spin systems. Journal of
Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-023-03132-4
chicago: Sugimoto, Shoki, Sven Joscha Henheik, Volodymyr Riabov, and László Erdös.
“Eigenstate Thermalisation Hypothesis for Translation Invariant Spin Systems.”
Journal of Statistical Physics. Springer Nature, 2023. https://doi.org/10.1007/s10955-023-03132-4.
ieee: S. Sugimoto, S. J. Henheik, V. Riabov, and L. Erdös, “Eigenstate thermalisation
hypothesis for translation invariant spin systems,” Journal of Statistical
Physics, vol. 190, no. 7. Springer Nature, 2023.
ista: Sugimoto S, Henheik SJ, Riabov V, Erdös L. 2023. Eigenstate thermalisation
hypothesis for translation invariant spin systems. Journal of Statistical Physics.
190(7), 128.
mla: Sugimoto, Shoki, et al. “Eigenstate Thermalisation Hypothesis for Translation
Invariant Spin Systems.” Journal of Statistical Physics, vol. 190, no.
7, 128, Springer Nature, 2023, doi:10.1007/s10955-023-03132-4.
short: S. Sugimoto, S.J. Henheik, V. Riabov, L. Erdös, Journal of Statistical Physics
190 (2023).
date_created: 2023-07-30T22:01:02Z
date_published: 2023-07-21T00:00:00Z
date_updated: 2023-12-13T11:38:44Z
day: '21'
ddc:
- '510'
- '530'
department:
- _id: LaEr
doi: 10.1007/s10955-023-03132-4
ec_funded: 1
external_id:
arxiv:
- '2304.04213'
isi:
- '001035677200002'
file:
- access_level: open_access
checksum: c2ef6b2aecfee1ad6d03fab620507c2c
content_type: application/pdf
creator: dernst
date_created: 2023-07-31T07:49:31Z
date_updated: 2023-07-31T07:49:31Z
file_id: '13325'
file_name: 2023_JourStatPhysics_Sugimoto.pdf
file_size: 612755
relation: main_file
success: 1
file_date_updated: 2023-07-31T07:49:31Z
has_accepted_license: '1'
intvolume: ' 190'
isi: 1
issue: '7'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Journal of Statistical Physics
publication_identifier:
eissn:
- 1572-9613
issn:
- 0022-4715
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Eigenstate thermalisation hypothesis for translation invariant spin systems
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 190
year: '2023'
...
---
_id: '12683'
abstract:
- lang: eng
text: We study the eigenvalue trajectories of a time dependent matrix Gt=H+itvv∗
for t≥0, where H is an N×N Hermitian random matrix and v is a unit vector. In
particular, we establish that with high probability, an outlier can be distinguished
at all times t>1+N−1/3+ϵ, for any ϵ>0. The study of this natural process combines
elements of Hermitian and non-Hermitian analysis, and illustrates some aspects
of the intrinsic instability of (even weakly) non-Hermitian matrices.
acknowledgement: G. Dubach gratefully acknowledges funding from the European Union’s
Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
Grant Agreement No. 754411. L. Erdős is supported by ERC Advanced Grant “RMTBeyond”
No. 101020331.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Guillaume
full_name: Dubach, Guillaume
id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E
last_name: Dubach
orcid: 0000-0001-6892-8137
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
citation:
ama: Dubach G, Erdös L. Dynamics of a rank-one perturbation of a Hermitian matrix.
Electronic Communications in Probability. 2023;28:1-13. doi:10.1214/23-ECP516
apa: Dubach, G., & Erdös, L. (2023). Dynamics of a rank-one perturbation of
a Hermitian matrix. Electronic Communications in Probability. Institute
of Mathematical Statistics. https://doi.org/10.1214/23-ECP516
chicago: Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation
of a Hermitian Matrix.” Electronic Communications in Probability. Institute
of Mathematical Statistics, 2023. https://doi.org/10.1214/23-ECP516.
ieee: G. Dubach and L. Erdös, “Dynamics of a rank-one perturbation of a Hermitian
matrix,” Electronic Communications in Probability, vol. 28. Institute of
Mathematical Statistics, pp. 1–13, 2023.
ista: Dubach G, Erdös L. 2023. Dynamics of a rank-one perturbation of a Hermitian
matrix. Electronic Communications in Probability. 28, 1–13.
mla: Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of
a Hermitian Matrix.” Electronic Communications in Probability, vol. 28,
Institute of Mathematical Statistics, 2023, pp. 1–13, doi:10.1214/23-ECP516.
short: G. Dubach, L. Erdös, Electronic Communications in Probability 28 (2023) 1–13.
date_created: 2023-02-26T23:01:01Z
date_published: 2023-02-08T00:00:00Z
date_updated: 2023-10-17T12:48:10Z
day: '08'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1214/23-ECP516
ec_funded: 1
external_id:
arxiv:
- '2108.13694'
isi:
- '000950650200005'
file:
- access_level: open_access
checksum: a1c6f0a3e33688fd71309c86a9aad86e
content_type: application/pdf
creator: dernst
date_created: 2023-02-27T09:43:27Z
date_updated: 2023-02-27T09:43:27Z
file_id: '12692'
file_name: 2023_ElectCommProbability_Dubach.pdf
file_size: 479105
relation: main_file
success: 1
file_date_updated: 2023-02-27T09:43:27Z
has_accepted_license: '1'
intvolume: ' 28'
isi: 1
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 1-13
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Electronic Communications in Probability
publication_identifier:
eissn:
- 1083-589X
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Dynamics of a rank-one perturbation of a Hermitian matrix
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2023'
...
---
_id: '12707'
abstract:
- lang: eng
text: We establish precise right-tail small deviation estimates for the largest
eigenvalue of real symmetric and complex Hermitian matrices whose entries are
independent random variables with uniformly bounded moments. The proof relies
on a Green function comparison along a continuous interpolating matrix flow for
a long time. Less precise estimates are also obtained in the left tail.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Yuanyuan
full_name: Xu, Yuanyuan
id: 7902bdb1-a2a4-11eb-a164-c9216f71aea3
last_name: Xu
orcid: 0000-0003-1559-1205
citation:
ama: Erdös L, Xu Y. Small deviation estimates for the largest eigenvalue of Wigner
matrices. Bernoulli. 2023;29(2):1063-1079. doi:10.3150/22-BEJ1490
apa: Erdös, L., & Xu, Y. (2023). Small deviation estimates for the largest eigenvalue
of Wigner matrices. Bernoulli. Bernoulli Society for Mathematical Statistics
and Probability. https://doi.org/10.3150/22-BEJ1490
chicago: Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest
Eigenvalue of Wigner Matrices.” Bernoulli. Bernoulli Society for Mathematical
Statistics and Probability, 2023. https://doi.org/10.3150/22-BEJ1490.
ieee: L. Erdös and Y. Xu, “Small deviation estimates for the largest eigenvalue
of Wigner matrices,” Bernoulli, vol. 29, no. 2. Bernoulli Society for Mathematical
Statistics and Probability, pp. 1063–1079, 2023.
ista: Erdös L, Xu Y. 2023. Small deviation estimates for the largest eigenvalue
of Wigner matrices. Bernoulli. 29(2), 1063–1079.
mla: Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest
Eigenvalue of Wigner Matrices.” Bernoulli, vol. 29, no. 2, Bernoulli Society
for Mathematical Statistics and Probability, 2023, pp. 1063–79, doi:10.3150/22-BEJ1490.
short: L. Erdös, Y. Xu, Bernoulli 29 (2023) 1063–1079.
date_created: 2023-03-05T23:01:05Z
date_published: 2023-05-01T00:00:00Z
date_updated: 2023-10-04T10:21:07Z
day: '01'
department:
- _id: LaEr
doi: 10.3150/22-BEJ1490
ec_funded: 1
external_id:
arxiv:
- '2112.12093 '
isi:
- '000947270100008'
intvolume: ' 29'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2112.12093
month: '05'
oa: 1
oa_version: Preprint
page: 1063-1079
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Bernoulli
publication_identifier:
issn:
- 1350-7265
publication_status: published
publisher: Bernoulli Society for Mathematical Statistics and Probability
quality_controlled: '1'
scopus_import: '1'
status: public
title: Small deviation estimates for the largest eigenvalue of Wigner matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 29
year: '2023'
...
---
_id: '12761'
abstract:
- lang: eng
text: "We consider the fluctuations of regular functions f of a Wigner matrix W
viewed as an entire matrix f (W). Going beyond the well-studied tracial mode,
Trf (W), which is equivalent to the customary linear statistics of eigenvalues,
we show that Trf (W)A is asymptotically normal for any nontrivial bounded deterministic
matrix A. We identify three different and asymptotically independent modes of
this fluctuation, corresponding to the tracial part, the traceless diagonal part
and the off-diagonal part of f (W) in the entire mesoscopic regime, where we find
that the off-diagonal modes fluctuate on a much smaller scale than the tracial
mode. As a main motivation to study CLT in such generality on small mesoscopic
scales, we determine\r\nthe fluctuations in the eigenstate thermalization hypothesis
(Phys. Rev. A 43 (1991) 2046–2049), that is, prove that the eigenfunction overlaps
with any deterministic matrix are asymptotically Gaussian after a small spectral
averaging. Finally, in the macroscopic regime our result also generalizes (Zh.
Mat. Fiz. Anal. Geom. 9 (2013) 536–581, 611, 615) to complex W and to all crossover
ensembles in between. The main technical inputs are the recent\r\nmultiresolvent
local laws with traceless deterministic matrices from the companion paper (Comm.
Math. Phys. 388 (2021) 1005–1048)."
acknowledgement: The second author is partially funded by the ERC Advanced Grant “RMTBEYOND”
No. 101020331. The third author is supported by Dr. Max Rössler, the Walter Haefner
Foundation and the ETH Zürich Foundation.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: Cipolloni G, Erdös L, Schröder DJ. Functional central limit theorems for Wigner
matrices. Annals of Applied Probability. 2023;33(1):447-489. doi:10.1214/22-AAP1820
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). Functional central
limit theorems for Wigner matrices. Annals of Applied Probability. Institute
of Mathematical Statistics. https://doi.org/10.1214/22-AAP1820
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Functional Central
Limit Theorems for Wigner Matrices.” Annals of Applied Probability. Institute
of Mathematical Statistics, 2023. https://doi.org/10.1214/22-AAP1820.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Functional central limit theorems
for Wigner matrices,” Annals of Applied Probability, vol. 33, no. 1. Institute
of Mathematical Statistics, pp. 447–489, 2023.
ista: Cipolloni G, Erdös L, Schröder DJ. 2023. Functional central limit theorems
for Wigner matrices. Annals of Applied Probability. 33(1), 447–489.
mla: Cipolloni, Giorgio, et al. “Functional Central Limit Theorems for Wigner Matrices.”
Annals of Applied Probability, vol. 33, no. 1, Institute of Mathematical
Statistics, 2023, pp. 447–89, doi:10.1214/22-AAP1820.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Applied Probability 33 (2023)
447–489.
date_created: 2023-03-26T22:01:08Z
date_published: 2023-02-01T00:00:00Z
date_updated: 2023-10-17T12:48:52Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/22-AAP1820
ec_funded: 1
external_id:
arxiv:
- '2012.13218'
isi:
- '000946432400015'
intvolume: ' 33'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2012.13218
month: '02'
oa: 1
oa_version: Preprint
page: 447-489
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Annals of Applied Probability
publication_identifier:
issn:
- 1050-5164
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Functional central limit theorems for Wigner matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 33
year: '2023'
...
---
_id: '12792'
abstract:
- lang: eng
text: In the physics literature the spectral form factor (SFF), the squared Fourier
transform of the empirical eigenvalue density, is the most common tool to test
universality for disordered quantum systems, yet previous mathematical results
have been restricted only to two exactly solvable models (Forrester in J Stat
Phys 183:33, 2021. https://doi.org/10.1007/s10955-021-02767-5, Commun Math Phys
387:215–235, 2021. https://doi.org/10.1007/s00220-021-04193-w). We rigorously
prove the physics prediction on SFF up to an intermediate time scale for a large
class of random matrices using a robust method, the multi-resolvent local laws.
Beyond Wigner matrices we also consider the monoparametric ensemble and prove
that universality of SFF can already be triggered by a single random parameter,
supplementing the recently proven Wigner–Dyson universality (Cipolloni et al.
in Probab Theory Relat Fields, 2021. https://doi.org/10.1007/s00440-022-01156-7)
to larger spectral scales. Remarkably, extensive numerics indicates that our formulas
correctly predict the SFF in the entire slope-dip-ramp regime, as customarily
called in physics.
acknowledgement: "We are grateful to the authors of [25] for sharing with us their
insights and preliminary numerical results. We are especially thankful to Stephen
Shenker for very valuable advice over several email communications. Helpful comments
on the manuscript from Peter Forrester and from the anonymous referees are also
acknowledged.\r\nOpen access funding provided by Institute of Science and Technology
(IST Austria).\r\nLászló Erdős: Partially supported by ERC Advanced Grant \"RMTBeyond\"
No. 101020331. Dominik Schröder: Supported by Dr. Max Rössler, the Walter Haefner
Foundation and the ETH Zürich Foundation."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: Cipolloni G, Erdös L, Schröder DJ. On the spectral form factor for random matrices.
Communications in Mathematical Physics. 2023;401:1665-1700. doi:10.1007/s00220-023-04692-y
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). On the spectral form
factor for random matrices. Communications in Mathematical Physics. Springer
Nature. https://doi.org/10.1007/s00220-023-04692-y
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Spectral
Form Factor for Random Matrices.” Communications in Mathematical Physics.
Springer Nature, 2023. https://doi.org/10.1007/s00220-023-04692-y.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “On the spectral form factor for
random matrices,” Communications in Mathematical Physics, vol. 401. Springer
Nature, pp. 1665–1700, 2023.
ista: Cipolloni G, Erdös L, Schröder DJ. 2023. On the spectral form factor for random
matrices. Communications in Mathematical Physics. 401, 1665–1700.
mla: Cipolloni, Giorgio, et al. “On the Spectral Form Factor for Random Matrices.”
Communications in Mathematical Physics, vol. 401, Springer Nature, 2023,
pp. 1665–700, doi:10.1007/s00220-023-04692-y.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics
401 (2023) 1665–1700.
date_created: 2023-04-02T22:01:11Z
date_published: 2023-07-01T00:00:00Z
date_updated: 2023-10-04T12:10:31Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00220-023-04692-y
ec_funded: 1
external_id:
isi:
- '000957343500001'
file:
- access_level: open_access
checksum: 72057940f76654050ca84a221f21786c
content_type: application/pdf
creator: dernst
date_created: 2023-10-04T12:09:18Z
date_updated: 2023-10-04T12:09:18Z
file_id: '14397'
file_name: 2023_CommMathPhysics_Cipolloni.pdf
file_size: 859967
relation: main_file
success: 1
file_date_updated: 2023-10-04T12:09:18Z
has_accepted_license: '1'
intvolume: ' 401'
isi: 1
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 1665-1700
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the spectral form factor for random matrices
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 401
year: '2023'
...
---
_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
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: 2023-08-03T06:34:24Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00220-022-04377-y
ec_funded: 1
external_id:
arxiv:
- '2102.04330'
isi:
- '000782737200001'
file:
- access_level: open_access
checksum: bee0278c5efa9a33d9a2dc8d354a6c51
content_type: application/pdf
creator: dernst
date_created: 2022-08-05T06:01:13Z
date_updated: 2022-08-05T06:01:13Z
file_id: '11726'
file_name: 2022_CommunMathPhys_Schnelli.pdf
file_size: 1141462
relation: main_file
success: 1
file_date_updated: 2022-08-05T06:01:13Z
has_accepted_license: '1'
intvolume: ' 393'
isi: 1
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
page: 839-907
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 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
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: 393
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).
date_created: 2022-08-05T11:36:56Z
date_published: 2022-07-29T00:00:00Z
date_updated: 2023-09-05T14:57:49Z
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'
file:
- access_level: open_access
checksum: b398c4dbf65f71d417981d6e366427e9
content_type: application/pdf
creator: dernst
date_created: 2022-08-08T07:36:34Z
date_updated: 2022-08-08T07:36:34Z
file_id: '11746'
file_name: 2022_JourStatisticalPhysics_Henheik.pdf
file_size: 419563
relation: main_file
success: 1
file_date_updated: 2022-08-08T07:36:34Z
has_accepted_license: '1'
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'
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: '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: 2023-08-02T13:44:32Z
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'
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: '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).
date_created: 2022-01-13T15:40:53Z
date_published: 2022-01-11T00:00:00Z
date_updated: 2023-08-02T13:51:52Z
day: '11'
ddc:
- '514'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1007/s11040-021-09415-0
ec_funded: 1
external_id:
arxiv:
- '2106.02015'
isi:
- '000741387600001'
file:
- access_level: open_access
checksum: d44f8123a52592a75b2c3b8ee2cd2435
content_type: application/pdf
creator: cchlebak
date_created: 2022-01-14T07:27:45Z
date_updated: 2022-01-14T07:27:45Z
file_id: '10624'
file_name: 2022_MathPhyAnalGeo_Henheik.pdf
file_size: 505804
relation: main_file
success: 1
file_date_updated: 2022-01-14T07:27:45Z
has_accepted_license: '1'
intvolume: ' 25'
isi: 1
issue: '1'
keyword:
- geometry and topology
- mathematical physics
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
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Mathematical Physics, Analysis and Geometry
publication_identifier:
eissn:
- 1572-9656
issn:
- 1385-0172
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The BCS critical temperature 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 25
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: 2023-08-02T13:57:02Z
day: '18'
ddc:
- '530'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1007/s11005-021-01494-y
ec_funded: 1
external_id:
arxiv:
- '2106.13780'
isi:
- '000744930400001'
file:
- access_level: open_access
checksum: 7e8e69b76e892c305071a4736131fe18
content_type: application/pdf
creator: cchlebak
date_created: 2022-01-19T09:41:14Z
date_updated: 2022-01-19T09:41:14Z
file_id: '10647'
file_name: 2022_LettersMathPhys_Henheik.pdf
file_size: 357547
relation: main_file
success: 1
file_date_updated: 2022-01-19T09:41:14Z
has_accepted_license: '1'
intvolume: ' 112'
isi: 1
issue: '1'
keyword:
- mathematical physics
- statistical and nonlinear physics
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: Letters in Mathematical Physics
publication_identifier:
eissn:
- 1573-0530
issn:
- 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 112
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).
date_created: 2022-01-18T16:18:51Z
date_published: 2022-01-18T00:00:00Z
date_updated: 2023-08-02T13:53:11Z
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'
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'
...