---
_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.
corr_author: '1'
date_created: 2024-01-08T13:03:18Z
date_published: 2023-08-01T00:00:00Z
date_updated: 2025-09-09T14:12:00Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/22-aap1882
ec_funded: 1
external_id:
arxiv:
- '2010.16083'
isi:
- '001031710500012'
intvolume: ' 33'
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.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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
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.
corr_author: '1'
date_created: 2024-01-10T09:23:31Z
date_published: 2023-02-01T00:00:00Z
date_updated: 2025-04-14T07:57:19Z
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: 2025-07-16T08:01:03Z
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
license: https://creativecommons.org/licenses/by/4.0/
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'
scopus_import: '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: 3E5EF7F0-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.
corr_author: '1'
date_created: 2024-01-22T08:08:41Z
date_published: 2023-11-01T00:00:00Z
date_updated: 2025-09-09T14:23:34Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/23-aop1643
ec_funded: 1
external_id:
arxiv:
- '2206.04448'
isi:
- '001112165000004'
intvolume: ' 51'
isi: 1
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'
scopus_import: '1'
status: public
title: On the rightmost eigenvalue of non-Hermitian random matrices
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 51
year: '2023'
...
---
_id: '10405'
abstract:
- lang: eng
text: 'We consider large non-Hermitian random matrices X with complex, independent,
identically distributed centred entries and show that the linear statistics of
their eigenvalues are asymptotically Gaussian for test functions having 2+ϵ derivatives.
Previously this result was known only for a few special cases; either the test
functions were required to be analytic [72], or the distribution of the matrix
elements needed to be Gaussian [73], or at least match the Gaussian up to the
first four moments [82, 56]. We find the exact dependence of the limiting variance
on the fourth cumulant that was not known before. The proof relies on two novel
ingredients: (i) a local law for a product of two resolvents of the Hermitisation
of X with different spectral parameters and (ii) a coupling of several weakly
dependent Dyson Brownian motions. These methods are also the key inputs for our
analogous results on the linear eigenvalue statistics of real matrices X that
are presented in the companion paper [32]. '
acknowledgement: L.E. would like to thank Nathanaël Berestycki and D.S.would like
to thank Nina Holden for valuable discussions on the Gaussian freefield.G.C. and
L.E. are partially supported by ERC Advanced Grant No. 338804.G.C. received funding
from the European Union’s Horizon 2020 research and in-novation programme under
the Marie Skłodowska-Curie Grant Agreement No.665385. D.S. is supported by Dr. Max
Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation.
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. Central limit theorem for linear eigenvalue
statistics of non-Hermitian random matrices. Communications on Pure and Applied
Mathematics. 2023;76(5):946-1034. doi:10.1002/cpa.22028
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). Central limit theorem
for linear eigenvalue statistics of non-Hermitian random matrices. Communications
on Pure and Applied Mathematics. Wiley. https://doi.org/10.1002/cpa.22028
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Central Limit
Theorem for Linear Eigenvalue Statistics of Non-Hermitian Random Matrices.” Communications
on Pure and Applied Mathematics. Wiley, 2023. https://doi.org/10.1002/cpa.22028.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Central limit theorem for linear
eigenvalue statistics of non-Hermitian random matrices,” Communications on
Pure and Applied Mathematics, vol. 76, no. 5. Wiley, pp. 946–1034, 2023.
ista: Cipolloni G, Erdös L, Schröder DJ. 2023. Central limit theorem for linear
eigenvalue statistics of non-Hermitian random matrices. Communications on Pure
and Applied Mathematics. 76(5), 946–1034.
mla: Cipolloni, Giorgio, et al. “Central Limit Theorem for Linear Eigenvalue Statistics
of Non-Hermitian Random Matrices.” Communications on Pure and Applied Mathematics,
vol. 76, no. 5, Wiley, 2023, pp. 946–1034, doi:10.1002/cpa.22028.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Communications on Pure and Applied
Mathematics 76 (2023) 946–1034.
corr_author: '1'
date_created: 2021-12-05T23:01:41Z
date_published: 2023-05-01T00:00:00Z
date_updated: 2025-03-31T16:00:54Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1002/cpa.22028
ec_funded: 1
external_id:
arxiv:
- '1912.04100'
isi:
- '000724652500001'
file:
- access_level: open_access
checksum: 8346bc2642afb4ccb7f38979f41df5d9
content_type: application/pdf
creator: dernst
date_created: 2023-10-04T09:21:48Z
date_updated: 2023-10-04T09:21:48Z
file_id: '14388'
file_name: 2023_CommPureMathematics_Cipolloni.pdf
file_size: 803440
relation: main_file
success: 1
file_date_updated: 2023-10-04T09:21:48Z
has_accepted_license: '1'
intvolume: ' 76'
isi: 1
issue: '5'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-nd/4.0/
month: '05'
oa: 1
oa_version: Published Version
page: 946-1034
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: Communications on Pure and Applied Mathematics
publication_identifier:
eissn:
- 1097-0312
issn:
- 0010-3640
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: Central limit theorem for linear eigenvalue statistics of non-Hermitian random
matrices
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 76
year: '2023'
...
---
_id: '17079'
abstract:
- lang: eng
text: We study moments of characteristic polynomials of truncated Haar distributed
matrices from the three classical compact groups O(N), U(N) and Sp(2N). For finite
matrix size we calculate the moments in terms of hypergeometric functions of matrix
argument and give explicit integral representations highlighting the duality between
the moment and the matrix size as well as the duality between the orthogonal and
symplectic cases. Asymptotic expansions in strong and weak non-unitarity regimes
are obtained. Using the connection to matrix hypergeometric functions, we establish
limit theorems for the log-modulus of the characteristic polynomial evaluated
on the unit circle.
acknowledgement: N.S. gratefully acknowledges financial support of the Royal Society,
grant URF/R1/180707. We would like to thank Emma Bailey, Yan Fyodorov and Jordan
Stoyanov for helpful comments an an earlier version of this paper. We are grateful
for the comments of an anonymous referee.
article_number: '2250049'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Alexander
full_name: Serebryakov, Alexander
last_name: Serebryakov
- first_name: Nick
full_name: Simm, Nick
last_name: Simm
- first_name: Guillaume
full_name: Dubach, Guillaume
id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E
last_name: Dubach
orcid: 0000-0001-6892-8137
citation:
ama: 'Serebryakov A, Simm N, Dubach G. Characteristic polynomials of random truncations:
Moments, duality and asymptotics. Random Matrices: Theory and Applications.
2023;12(01). doi:10.1142/s2010326322500496'
apa: 'Serebryakov, A., Simm, N., & Dubach, G. (2023). Characteristic polynomials
of random truncations: Moments, duality and asymptotics. Random Matrices: Theory
and Applications. World Scientific Publishing. https://doi.org/10.1142/s2010326322500496'
chicago: 'Serebryakov, Alexander, Nick Simm, and Guillaume Dubach. “Characteristic
Polynomials of Random Truncations: Moments, Duality and Asymptotics.” Random
Matrices: Theory and Applications. World Scientific Publishing, 2023. https://doi.org/10.1142/s2010326322500496.'
ieee: 'A. Serebryakov, N. Simm, and G. Dubach, “Characteristic polynomials of random
truncations: Moments, duality and asymptotics,” Random Matrices: Theory and
Applications, vol. 12, no. 01. World Scientific Publishing, 2023.'
ista: 'Serebryakov A, Simm N, Dubach G. 2023. Characteristic polynomials of random
truncations: Moments, duality and asymptotics. Random Matrices: Theory and Applications.
12(01), 2250049.'
mla: 'Serebryakov, Alexander, et al. “Characteristic Polynomials of Random Truncations:
Moments, Duality and Asymptotics.” Random Matrices: Theory and Applications,
vol. 12, no. 01, 2250049, World Scientific Publishing, 2023, doi:10.1142/s2010326322500496.'
short: 'A. Serebryakov, N. Simm, G. Dubach, Random Matrices: Theory and Applications
12 (2023).'
date_created: 2024-05-29T06:14:26Z
date_published: 2023-01-01T00:00:00Z
date_updated: 2025-09-09T14:27:10Z
day: '01'
department:
- _id: LaEr
doi: 10.1142/s2010326322500496
external_id:
arxiv:
- '2109.10331'
isi:
- '000848874400001'
intvolume: ' 12'
isi: 1
issue: '01'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2109.10331
month: '01'
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'
scopus_import: '1'
status: public
title: 'Characteristic polynomials of random truncations: Moments, duality and asymptotics'
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 12
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).'
corr_author: '1'
date_created: 2023-10-12T12:42:53Z
date_published: 2023-10-11T00:00:00Z
date_updated: 2026-04-07T12:37:10Z
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'
related_material:
record:
- id: '19540'
relation: dissertation_contains
status: public
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: '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: 2026-04-07T12:37:10Z
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'
related_material:
record:
- id: '20575'
relation: dissertation_contains
status: public
- id: '19540'
relation: dissertation_contains
status: public
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: '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
orcid: 0000-0003-1491-4623
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).
corr_author: '1'
date_created: 2023-09-17T22:01:09Z
date_published: 2023-08-23T00:00:00Z
date_updated: 2026-04-07T12:37:10Z
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'
related_material:
record:
- id: '19540'
relation: dissertation_contains
status: public
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'
...
---
OA_place: repository
_id: '17174'
abstract:
- lang: eng
text: We prove that a class of weakly perturbed Hamiltonians of the form $H_λ= H_0
+ λW$, with $W$ being a Wigner matrix, exhibits prethermalization. That is, the
time evolution generated by $H_λ$ relaxes to its ultimate thermal state via an
intermediate prethermal state with a lifetime of order $λ^{-2}$. Moreover, we
obtain a general relaxation formula, expressing the perturbed dynamics via the
unperturbed dynamics and the ultimate thermal state. The proof relies on a two-resolvent
law for the deformed Wigner matrix $H_λ$.
article_number: '2310.06677'
article_processing_charge: No
arxiv: 1
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- first_name: Jana
full_name: Reker, Jana
id: e796e4f9-dc8d-11ea-abe3-97e26a0323e9
last_name: Reker
- first_name: Volodymyr
full_name: Riabov, Volodymyr
id: 1949f904-edfb-11eb-afb5-e2dfddabb93b
last_name: Riabov
citation:
ama: Erdös L, Henheik SJ, Reker J, Riabov V. Prethermalization for deformed Wigner
Matrices. arXiv. doi:10.48550/arXiv.2310.06677
apa: Erdös, L., Henheik, S. J., Reker, J., & Riabov, V. (n.d.). Prethermalization
for deformed Wigner Matrices. arXiv. https://doi.org/10.48550/arXiv.2310.06677
chicago: Erdös, László, Sven Joscha Henheik, Jana Reker, and Volodymyr Riabov. “Prethermalization
for Deformed Wigner Matrices.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2310.06677.
ieee: L. Erdös, S. J. Henheik, J. Reker, and V. Riabov, “Prethermalization for deformed
Wigner Matrices,” arXiv. .
ista: Erdös L, Henheik SJ, Reker J, Riabov V. Prethermalization for deformed Wigner
Matrices. arXiv, 2310.06677.
mla: Erdös, László, et al. “Prethermalization for Deformed Wigner Matrices.” ArXiv,
2310.06677, doi:10.48550/arXiv.2310.06677.
short: L. Erdös, S.J. Henheik, J. Reker, V. Riabov, ArXiv (n.d.).
corr_author: '1'
date_created: 2024-06-26T08:56:52Z
date_published: 2023-12-23T00:00:00Z
date_updated: 2026-04-07T13:02:12Z
day: '23'
department:
- _id: LaEr
doi: 10.48550/arXiv.2310.06677
ec_funded: 1
external_id:
arxiv:
- '2310.06677'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2310.06677
month: '12'
oa: 1
oa_version: Preprint
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: arXiv
publication_status: draft
related_material:
record:
- id: '18764'
relation: later_version
status: public
- id: '20575'
relation: dissertation_contains
status: public
- id: '17164'
relation: dissertation_contains
status: public
status: public
title: Prethermalization for deformed Wigner Matrices
type: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2023'
...
---
OA_place: repository
_id: '17173'
abstract:
- lang: eng
text: Consider the random variable $\mathrm{Tr}( f_1(W)A_1\dots f_k(W)A_k)$ where
$W$ is an $N\times N$ Hermitian Wigner matrix, $k\in\mathbb{N}$, and choose (possibly
$N$-dependent) regular functions $f_1,\dots, f_k$ as well as bounded deterministic
matrices $A_1,\dots,A_k$. We give a functional central limit theorem showing that
the fluctuations around the expectation are Gaussian. Moreover, we determine the
limiting covariance structure and give explicit error bounds in terms of the scaling
of $f_1,\dots,f_k$ and the number of traceless matrices among $A_1,\dots,A_k$,
thus extending the results of [Cipolloni, Erdős, Schröder 2023] to products of
arbitrary length $k\geq2$. As an application, we consider the fluctuation of $\mathrm{Tr}(\mathrm{e}^{\mathrm{i}
tW}A_1\mathrm{e}^{-\mathrm{i} tW}A_2)$ around its thermal value $\mathrm{Tr}(A_1)\mathrm{Tr}(A_2)$
when $t$ is large and give an explicit formula for the variance.
article_number: '2307.11028'
article_processing_charge: No
arxiv: 1
author:
- first_name: Jana
full_name: Reker, Jana
id: e796e4f9-dc8d-11ea-abe3-97e26a0323e9
last_name: Reker
citation:
ama: Reker J. Multi-point functional central limit theorem for Wigner Matrices.
arXiv. doi:10.48550/arXiv.2307.11028
apa: Reker, J. (n.d.). Multi-point functional central limit theorem for Wigner Matrices.
arXiv. https://doi.org/10.48550/arXiv.2307.11028
chicago: Reker, Jana. “Multi-Point Functional Central Limit Theorem for Wigner Matrices.”
ArXiv, n.d. https://doi.org/10.48550/arXiv.2307.11028.
ieee: J. Reker, “Multi-point functional central limit theorem for Wigner Matrices,”
arXiv. .
ista: Reker J. Multi-point functional central limit theorem for Wigner Matrices.
arXiv, 2307.11028.
mla: Reker, Jana. “Multi-Point Functional Central Limit Theorem for Wigner Matrices.”
ArXiv, 2307.11028, doi:10.48550/arXiv.2307.11028.
short: J. Reker, ArXiv (n.d.).
date_created: 2024-06-26T08:54:56Z
date_published: 2023-07-21T00:00:00Z
date_updated: 2026-04-07T13:02:12Z
day: '21'
department:
- _id: LaEr
doi: 10.48550/arXiv.2307.11028
external_id:
arxiv:
- '2307.11028'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2307.11028
month: '07'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: draft
related_material:
record:
- id: '18762'
relation: later_version
status: public
- id: '17164'
relation: dissertation_contains
status: public
status: public
title: Multi-point functional central limit theorem for Wigner Matrices
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '12110'
abstract:
- lang: eng
text: A recently proposed approach for avoiding the ultraviolet divergence of Hamiltonians
with particle creation is based on interior-boundary conditions (IBCs). The approach
works well in the non-relativistic case, i.e., for the Laplacian operator. Here,
we study how the approach can be applied to Dirac operators. While this has successfully
been done already in one space dimension, and more generally for codimension-1
boundaries, the situation of point sources in three dimensions corresponds to
a codimension-3 boundary. One would expect that, for such a boundary, Dirac operators
do not allow for boundary conditions because they are known not to allow for point
interactions in 3D, which also correspond to a boundary condition. Indeed, we
confirm this expectation here by proving that there is no self-adjoint operator
on a (truncated) Fock space that would correspond to a Dirac operator with an
IBC at configurations with a particle at the origin. However, we also present
a positive result showing that there are self-adjoint operators with an IBC (on
the boundary consisting of configurations with a particle at the origin) that
are away from those configurations, given by a Dirac operator plus a sufficiently
strong Coulomb potential.
acknowledgement: "J.H. gratefully acknowledges the partial financial support by the
ERC Advanced Grant “RMTBeyond” under Grant No. 101020331.\r\n"
article_number: '122302'
article_processing_charge: No
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: Roderich
full_name: Tumulka, Roderich
last_name: Tumulka
citation:
ama: Henheik SJ, Tumulka R. Interior-boundary conditions for the Dirac equation
at point sources in three dimensions. Journal of Mathematical Physics.
2022;63(12). doi:10.1063/5.0104675
apa: Henheik, S. J., & Tumulka, R. (2022). Interior-boundary conditions for
the Dirac equation at point sources in three dimensions. Journal of Mathematical
Physics. AIP Publishing. https://doi.org/10.1063/5.0104675
chicago: Henheik, Sven Joscha, and Roderich Tumulka. “Interior-Boundary Conditions
for the Dirac Equation at Point Sources in Three Dimensions.” Journal of Mathematical
Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0104675.
ieee: S. J. Henheik and R. Tumulka, “Interior-boundary conditions for the Dirac
equation at point sources in three dimensions,” Journal of Mathematical Physics,
vol. 63, no. 12. AIP Publishing, 2022.
ista: Henheik SJ, Tumulka R. 2022. Interior-boundary conditions for the Dirac equation
at point sources in three dimensions. Journal of Mathematical Physics. 63(12),
122302.
mla: Henheik, Sven Joscha, and Roderich Tumulka. “Interior-Boundary Conditions for
the Dirac Equation at Point Sources in Three Dimensions.” Journal of Mathematical
Physics, vol. 63, no. 12, 122302, AIP Publishing, 2022, doi:10.1063/5.0104675.
short: S.J. Henheik, R. Tumulka, Journal of Mathematical Physics 63 (2022).
corr_author: '1'
date_created: 2023-01-08T23:00:53Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2025-04-14T07:57:18Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1063/5.0104675
ec_funded: 1
external_id:
isi:
- '000900748900002'
file:
- access_level: open_access
checksum: 5150287295e0ce4f12462c990744d65d
content_type: application/pdf
creator: dernst
date_created: 2023-01-20T11:58:59Z
date_updated: 2023-01-20T11:58:59Z
file_id: '12327'
file_name: 2022_JourMathPhysics_Henheik.pdf
file_size: 5436804
relation: main_file
success: 1
file_date_updated: 2023-01-20T11:58:59Z
has_accepted_license: '1'
intvolume: ' 63'
isi: 1
issue: '12'
language:
- iso: eng
month: '12'
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 Mathematical Physics
publication_identifier:
issn:
- 0022-2488
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Interior-boundary conditions for the Dirac equation at point sources in three
dimensions
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: '12148'
abstract:
- lang: eng
text: 'We prove a general local law for Wigner matrices that optimally handles observables
of arbitrary rank and thus unifies the well-known averaged and isotropic local
laws. As an application, we prove a central limit theorem in quantum unique ergodicity
(QUE): that is, we show that the quadratic forms of a general deterministic matrix
A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation.
For the bulk spectrum, we thus generalise our previous result [17] as valid for
test matrices A of large rank as well as the result of Benigni and Lopatto [7]
as valid for specific small-rank observables.'
acknowledgement: L.E. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331.
D.S. acknowledges the support of Dr. Max Rössler, the Walter Haefner Foundation
and the ETH Zürich Foundation.
article_number: e96
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. Rank-uniform local law for Wigner matrices.
Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2022.86
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Rank-uniform local
law for Wigner matrices. Forum of Mathematics, Sigma. Cambridge University
Press. https://doi.org/10.1017/fms.2022.86
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Rank-Uniform
Local Law for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge
University Press, 2022. https://doi.org/10.1017/fms.2022.86.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner
matrices,” Forum of Mathematics, Sigma, vol. 10. Cambridge University Press,
2022.
ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner
matrices. Forum of Mathematics, Sigma. 10, e96.
mla: Cipolloni, Giorgio, et al. “Rank-Uniform Local Law for Wigner Matrices.” Forum
of Mathematics, Sigma, vol. 10, e96, Cambridge University Press, 2022, doi:10.1017/fms.2022.86.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022).
corr_author: '1'
date_created: 2023-01-12T12:07:30Z
date_published: 2022-10-27T00:00:00Z
date_updated: 2025-04-14T07:57:18Z
day: '27'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1017/fms.2022.86
ec_funded: 1
external_id:
isi:
- '000873719200001'
file:
- access_level: open_access
checksum: 94a049aeb1eea5497aa097712a73c400
content_type: application/pdf
creator: dernst
date_created: 2023-01-24T10:02:40Z
date_updated: 2023-01-24T10:02:40Z
file_id: '12356'
file_name: 2022_ForumMath_Cipolloni.pdf
file_size: 817089
relation: main_file
success: 1
file_date_updated: 2023-01-24T10:02:40Z
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: '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: Forum of Mathematics, Sigma
publication_identifier:
issn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Rank-uniform local law 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: 10
year: '2022'
...
---
_id: '12179'
abstract:
- lang: eng
text: We derive an accurate lower tail estimate on the lowest singular value σ1(X−z)
of a real Gaussian (Ginibre) random matrix X shifted by a complex parameter z.
Such shift effectively changes the upper tail behavior of the condition number
κ(X−z) from the slower (κ(X−z)≥t)≲1/t decay typical for real Ginibre matrices
to the faster 1/t2 decay seen for complex Ginibre matrices as long as z is away
from the real axis. This sharpens and resolves a recent conjecture in [J. Banks
et al., https://arxiv.org/abs/2005.08930, 2020] on the regularizing effect of
the real Ginibre ensemble with a genuinely complex shift. As a consequence we
obtain an improved upper bound on the eigenvalue condition numbers (known also
as the eigenvector overlaps) for real Ginibre matrices. The main technical tool
is a rigorous supersymmetric analysis from our earlier work [Probab. Math. Phys.,
1 (2020), pp. 101--146].
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. On the condition number of the shifted real
Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. 2022;43(3):1469-1487.
doi:10.1137/21m1424408
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). On the condition number
of the shifted real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications.
Society for Industrial and Applied Mathematics. https://doi.org/10.1137/21m1424408
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Condition
Number of the Shifted Real Ginibre Ensemble.” SIAM Journal on Matrix Analysis
and Applications. Society for Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/21m1424408.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “On the condition number of the
shifted real Ginibre ensemble,” SIAM Journal on Matrix Analysis and Applications,
vol. 43, no. 3. Society for Industrial and Applied Mathematics, pp. 1469–1487,
2022.
ista: Cipolloni G, Erdös L, Schröder DJ. 2022. On the condition number of the shifted
real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. 43(3),
1469–1487.
mla: Cipolloni, Giorgio, et al. “On the Condition Number of the Shifted Real Ginibre
Ensemble.” SIAM Journal on Matrix Analysis and Applications, vol. 43, no.
3, Society for Industrial and Applied Mathematics, 2022, pp. 1469–87, doi:10.1137/21m1424408.
short: G. Cipolloni, L. Erdös, D.J. Schröder, SIAM Journal on Matrix Analysis and
Applications 43 (2022) 1469–1487.
corr_author: '1'
date_created: 2023-01-12T12:12:38Z
date_published: 2022-07-01T00:00:00Z
date_updated: 2025-09-10T09:51:27Z
day: '01'
department:
- _id: LaEr
doi: 10.1137/21m1424408
external_id:
arxiv:
- '2105.13719'
isi:
- '001125796400002'
intvolume: ' 43'
isi: 1
issue: '3'
keyword:
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2105.13719
month: '07'
oa: 1
oa_version: Preprint
page: 1469-1487
publication: SIAM Journal on Matrix Analysis and Applications
publication_identifier:
eissn:
- 1095-7162
issn:
- 0895-4798
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the condition number of the shifted real Ginibre ensemble
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 43
year: '2022'
...
---
_id: '12214'
abstract:
- lang: eng
text: 'Motivated by Kloeckner’s result on the isometry group of the quadratic Wasserstein
space W2(Rn), we describe the isometry group Isom(Wp(E)) for all parameters 0
< p < ∞ and for all separable real Hilbert spaces E. In particular, we show that
Wp(X) is isometrically rigid for all Polish space X whenever 0 < p < 1. This is
a consequence of our more general result: we prove that W1(X) is isometrically
rigid if X is a complete separable metric space that satisfies the strict triangle
inequality. Furthermore, we show that this latter rigidity result does not generalise
to parameters p > 1, by solving Kloeckner’s problem affirmatively on the existence
of mass-splitting isometries. '
acknowledgement: "Geher was supported by the Leverhulme Trust Early Career Fellowship
(ECF-2018-125), and also by the Hungarian National Research, Development and Innovation
Office - NKFIH (grant no. K115383 and K134944).\r\nTitkos was supported by the Hungarian
National Research, Development and Innovation Office - NKFIH (grant no. PD128374,
grant no. K115383 and K134944), by the J´anos Bolyai Research Scholarship of the
Hungarian Academy of Sciences, and by the UNKP-20-5-BGE-1 New National Excellence
Program of the ´Ministry of Innovation and Technology.\r\nVirosztek was supported
by the European Union’s Horizon 2020 research and innovation program under the Marie
Sklodowska-Curie Grant Agreement No. 846294, by the Momentum program of the Hungarian
Academy of Sciences under grant agreement no. LP2021-15/2021, and partially supported
by the Hungarian National Research, Development and Innovation Office - NKFIH (grants
no. K124152 and no. KH129601). "
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: György Pál
full_name: Gehér, György Pál
last_name: Gehér
- first_name: Tamás
full_name: Titkos, Tamás
last_name: Titkos
- first_name: Daniel
full_name: Virosztek, Daniel
id: 48DB45DA-F248-11E8-B48F-1D18A9856A87
last_name: Virosztek
orcid: 0000-0003-1109-5511
citation:
ama: 'Gehér GP, Titkos T, Virosztek D. The isometry group of Wasserstein spaces:
The Hilbertian case. Journal of the London Mathematical Society. 2022;106(4):3865-3894.
doi:10.1112/jlms.12676'
apa: 'Gehér, G. P., Titkos, T., & Virosztek, D. (2022). The isometry group of
Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical
Society. Wiley. https://doi.org/10.1112/jlms.12676'
chicago: 'Gehér, György Pál, Tamás Titkos, and Daniel Virosztek. “The Isometry Group
of Wasserstein Spaces: The Hilbertian Case.” Journal of the London Mathematical
Society. Wiley, 2022. https://doi.org/10.1112/jlms.12676.'
ieee: 'G. P. Gehér, T. Titkos, and D. Virosztek, “The isometry group of Wasserstein
spaces: The Hilbertian case,” Journal of the London Mathematical Society,
vol. 106, no. 4. Wiley, pp. 3865–3894, 2022.'
ista: 'Gehér GP, Titkos T, Virosztek D. 2022. The isometry group of Wasserstein
spaces: The Hilbertian case. Journal of the London Mathematical Society. 106(4),
3865–3894.'
mla: 'Gehér, György Pál, et al. “The Isometry Group of Wasserstein Spaces: The Hilbertian
Case.” Journal of the London Mathematical Society, vol. 106, no. 4, Wiley,
2022, pp. 3865–94, doi:10.1112/jlms.12676.'
short: G.P. Gehér, T. Titkos, D. Virosztek, Journal of the London Mathematical Society
106 (2022) 3865–3894.
date_created: 2023-01-16T09:46:13Z
date_published: 2022-09-18T00:00:00Z
date_updated: 2025-04-14T07:50:40Z
day: '18'
department:
- _id: LaEr
doi: 10.1112/jlms.12676
ec_funded: 1
external_id:
arxiv:
- '2102.02037'
isi:
- '000854878500001'
intvolume: ' 106'
isi: 1
issue: '4'
keyword:
- General Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2102.02037
month: '09'
oa: 1
oa_version: Preprint
page: 3865-3894
project:
- _id: 26A455A6-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '846294'
name: Geometric study of Wasserstein spaces and free probability
publication: Journal of the London Mathematical Society
publication_identifier:
eissn:
- 1469-7750
issn:
- 0024-6107
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'The isometry group of Wasserstein spaces: The Hilbertian case'
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 106
year: '2022'
...
---
_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
external_id:
isi:
- '000796323500001'
file:
- access_level: open_access
checksum: 5582f059feeb2f63e2eb68197a34d7dc
content_type: application/pdf
creator: dernst
date_created: 2023-01-27T11:06:47Z
date_updated: 2023-01-27T11:06:47Z
file_id: '12424'
file_name: 2022_AnnalesHenriP_Cipolloni.pdf
file_size: 1333638
relation: main_file
success: 1
file_date_updated: 2023-01-27T11:06:47Z
has_accepted_license: '1'
intvolume: ' 23'
isi: 1
issue: '11'
keyword:
- Mathematical Physics
- Nuclear and High Energy Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
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:
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- '530'
department:
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doi: 10.1063/5.0104290
ec_funded: 1
external_id:
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- '2206.04443'
isi:
- '000869715800001'
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name: Random matrices beyond Wigner-Dyson-Mehta
publication: Journal of Mathematical Physics
publication_identifier:
eissn:
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title: Directional extremal statistics for Ginibre eigenvalues
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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:
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department:
- _id: LaEr
doi: 10.1214/22-ejp838
ec_funded: 1
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isi:
- '000910863700003'
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file_size: 502149
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file_date_updated: 2023-01-30T11:59:21Z
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intvolume: ' 27'
isi: 1
keyword:
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- Probability and Uncertainty
- Statistics and Probability
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 1-38
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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:
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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:
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checksum: 87592a755adcef22ea590a99dc728dd3
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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
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title: 'Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk'
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type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 10
year: '2022'
...