---
_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: '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: '11135'
abstract:
- lang: eng
text: We consider a correlated NxN Hermitian random matrix with a polynomially decaying
metric correlation structure. By calculating the trace of the moments of the matrix
and using the summable decay of the cumulants, we show that its operator norm
is stochastically dominated by one.
article_number: '2250036'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jana
full_name: Reker, Jana
id: e796e4f9-dc8d-11ea-abe3-97e26a0323e9
last_name: Reker
citation:
ama: 'Reker J. On the operator norm of a Hermitian random matrix with correlated
entries. Random Matrices: Theory and Applications. 2022;11(4). doi:10.1142/s2010326322500368'
apa: 'Reker, J. (2022). On the operator norm of a Hermitian random matrix with correlated
entries. Random Matrices: Theory and Applications. World Scientific. https://doi.org/10.1142/s2010326322500368'
chicago: 'Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated
Entries.” Random Matrices: Theory and Applications. World Scientific, 2022.
https://doi.org/10.1142/s2010326322500368.'
ieee: 'J. Reker, “On the operator norm of a Hermitian random matrix with correlated
entries,” Random Matrices: Theory and Applications, vol. 11, no. 4. World
Scientific, 2022.'
ista: 'Reker J. 2022. On the operator norm of a Hermitian random matrix with correlated
entries. Random Matrices: Theory and Applications. 11(4), 2250036.'
mla: 'Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated
Entries.” Random Matrices: Theory and Applications, vol. 11, no. 4, 2250036,
World Scientific, 2022, doi:10.1142/s2010326322500368.'
short: 'J. Reker, Random Matrices: Theory and Applications 11 (2022).'
date_created: 2022-04-08T07:11:12Z
date_published: 2022-10-01T00:00:00Z
date_updated: 2023-08-03T06:32:22Z
day: '01'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1142/s2010326322500368
external_id:
arxiv:
- '2103.03906'
isi:
- '000848873800001'
intvolume: ' 11'
isi: 1
issue: '4'
keyword:
- Discrete Mathematics and Combinatorics
- Statistics
- Probability and Uncertainty
- Statistics and Probability
- Algebra and Number Theory
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2103.03906'
month: '10'
oa: 1
oa_version: Preprint
publication: 'Random Matrices: Theory and Applications'
publication_identifier:
eissn:
- 2010-3271
issn:
- 2010-3263
publication_status: published
publisher: World Scientific
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the operator norm of a Hermitian random matrix with correlated entries
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 11
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.
date_created: 2023-01-16T10:04:38Z
date_published: 2022-09-12T00:00:00Z
date_updated: 2023-08-04T10:32:23Z
day: '12'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1214/22-ejp838
ec_funded: 1
external_id:
isi:
- '000910863700003'
file:
- access_level: open_access
checksum: bb647b48fbdb59361210e425c220cdcb
content_type: application/pdf
creator: dernst
date_created: 2023-01-30T11:59:21Z
date_updated: 2023-01-30T11:59:21Z
file_id: '12464'
file_name: 2022_ElecJournProbability_Cipolloni.pdf
file_size: 502149
relation: main_file
success: 1
file_date_updated: 2023-01-30T11:59:21Z
has_accepted_license: '1'
intvolume: ' 27'
isi: 1
keyword:
- Statistics
- Probability and Uncertainty
- Statistics and Probability
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 1-38
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
call_identifier: H2020
grant_number: '101020331'
name: Random matrices beyond Wigner-Dyson-Mehta
publication: Electronic Journal of Probability
publication_identifier:
eissn:
- 1083-6489
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal multi-resolvent local laws for Wigner matrices
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 27
year: '2022'
...
---
_id: '12480'
abstract:
- lang: eng
text: 'We consider the problem of estimating a signal from measurements obtained
via a generalized linear model. We focus on estimators based on approximate message
passing (AMP), a family of iterative algorithms with many appealing features:
the performance of AMP in the high-dimensional limit can be succinctly characterized
under suitable model assumptions; AMP can also be tailored to the empirical distribution
of the signal entries, and for a wide class of estimation problems, AMP is conjectured
to be optimal among all polynomial-time algorithms. However, a major issue of
AMP is that in many models (such as phase retrieval), it requires an initialization
correlated with the ground-truth signal and independent from the measurement matrix.
Assuming that such an initialization is available is typically not realistic.
In this paper, we solve this problem by proposing an AMP algorithm initialized
with a spectral estimator. With such an initialization, the standard AMP analysis
fails since the spectral estimator depends in a complicated way on the design
matrix. Our main contribution is a rigorous characterization of the performance
of AMP with spectral initialization in the high-dimensional limit. The key technical
idea is to define and analyze a two-phase artificial AMP algorithm that first
produces the spectral estimator, and then closely approximates the iterates of
the true AMP. We also provide numerical results that demonstrate the validity
of the proposed approach.'
acknowledgement: "The authors would like to thank Andrea Montanari for helpful discussions.\r\nM
Mondelli was partially supported by the 2019 Lopez-Loreta Prize. R Venkataramanan
was partially supported by the Alan Turing Institute under the EPSRC Grant\r\nEP/N510129/1."
article_number: '114003'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: Ramji
full_name: Venkataramanan, Ramji
last_name: Venkataramanan
citation:
ama: 'Mondelli M, Venkataramanan R. Approximate message passing with spectral initialization
for generalized linear models. Journal of Statistical Mechanics: Theory and
Experiment. 2022;2022(11). doi:10.1088/1742-5468/ac9828'
apa: 'Mondelli, M., & Venkataramanan, R. (2022). Approximate message passing
with spectral initialization for generalized linear models. Journal of Statistical
Mechanics: Theory and Experiment. IOP Publishing. https://doi.org/10.1088/1742-5468/ac9828'
chicago: 'Mondelli, Marco, and Ramji Venkataramanan. “Approximate Message Passing
with Spectral Initialization for Generalized Linear Models.” Journal of Statistical
Mechanics: Theory and Experiment. IOP Publishing, 2022. https://doi.org/10.1088/1742-5468/ac9828.'
ieee: 'M. Mondelli and R. Venkataramanan, “Approximate message passing with spectral
initialization for generalized linear models,” Journal of Statistical Mechanics:
Theory and Experiment, vol. 2022, no. 11. IOP Publishing, 2022.'
ista: 'Mondelli M, Venkataramanan R. 2022. Approximate message passing with spectral
initialization for generalized linear models. Journal of Statistical Mechanics:
Theory and Experiment. 2022(11), 114003.'
mla: 'Mondelli, Marco, and Ramji Venkataramanan. “Approximate Message Passing with
Spectral Initialization for Generalized Linear Models.” Journal of Statistical
Mechanics: Theory and Experiment, vol. 2022, no. 11, 114003, IOP Publishing,
2022, doi:10.1088/1742-5468/ac9828.'
short: 'M. Mondelli, R. Venkataramanan, Journal of Statistical Mechanics: Theory
and Experiment 2022 (2022).'
date_created: 2023-02-02T08:31:57Z
date_published: 2022-11-24T00:00:00Z
date_updated: 2024-03-07T10:36:52Z
day: '24'
ddc:
- '510'
- '530'
department:
- _id: MaMo
doi: 10.1088/1742-5468/ac9828
external_id:
isi:
- '000889589900001'
file:
- access_level: open_access
checksum: 01411ffa76d3e380a0446baeb89b1ef7
content_type: application/pdf
creator: dernst
date_created: 2023-02-02T08:35:52Z
date_updated: 2023-02-02T08:35:52Z
file_id: '12481'
file_name: 2022_JourStatisticalMechanics_Mondelli.pdf
file_size: 1729997
relation: main_file
success: 1
file_date_updated: 2023-02-02T08:35:52Z
has_accepted_license: '1'
intvolume: ' 2022'
isi: 1
issue: '11'
keyword:
- Statistics
- Probability and Uncertainty
- Statistics and Probability
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: 'Journal of Statistical Mechanics: Theory and Experiment'
publication_identifier:
issn:
- 1742-5468
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
related_material:
record:
- id: '10598'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Approximate message passing with spectral initialization for generalized linear
models
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: 2022
year: '2022'
...
---
_id: '9158'
abstract:
- lang: eng
text: While several tools have been developed to study the ground state of many-body
quantum spin systems, the limitations of existing techniques call for the exploration
of new approaches. In this manuscript we develop an alternative analytical and
numerical framework for many-body quantum spin ground states, based on the disentanglement
formalism. In this approach, observables are exactly expressed as Gaussian-weighted
functional integrals over scalar fields. We identify the leading contribution
to these integrals, given by the saddle point of a suitable effective action.
Analytically, we develop a field-theoretical expansion of the functional integrals,
performed by means of appropriate Feynman rules. The expansion can be truncated
to a desired order to obtain analytical approximations to observables. Numerically,
we show that the disentanglement approach can be used to compute ground state
expectation values from classical stochastic processes. While the associated fluctuations
grow exponentially with imaginary time and the system size, this growth can be
mitigated by means of an importance sampling scheme based on knowledge of the
saddle point configuration. We illustrate the advantages and limitations of our
methods by considering the quantum Ising model in 1, 2 and 3 spatial dimensions.
Our analytical and numerical approaches are applicable to a broad class of systems,
bridging concepts from quantum lattice models, continuum field theory, and classical
stochastic processes.
acknowledgement: "S D N would like to thank M J Bhaseen, J Chalker, B Doyon, V Gritsev,
A Lamacraft,\r\nA Michailidis and M Serbyn for helpful feedback and stimulating
conversations. S D N\r\nacknowledges funding from the Institute of Science and Technology
(IST) Austria, and\r\nfrom the European Union’s Horizon 2020 research and innovation
program under the\r\nMarie Sk\blodowska-Curie Grant Agreement No. 754411. S D N
also acknowledges funding\r\nfrom the EPSRC Center for Doctoral Training in Cross-Disciplinary
Approaches to Non-\r\nEquilibrium Systems (CANES) under Grant EP/L015854/1. S D
N is grateful to IST\r\nAustria for providing open access funding."
article_number: '013101'
article_processing_charge: No
article_type: original
author:
- first_name: Stefano
full_name: De Nicola, Stefano
id: 42832B76-F248-11E8-B48F-1D18A9856A87
last_name: De Nicola
orcid: 0000-0002-4842-6671
citation:
ama: 'De Nicola S. Disentanglement approach to quantum spin ground states: Field
theory and stochastic simulation. Journal of Statistical Mechanics: Theory
and Experiment. 2021;2021(1). doi:10.1088/1742-5468/abc7c7'
apa: 'De Nicola, S. (2021). Disentanglement approach to quantum spin ground states:
Field theory and stochastic simulation. Journal of Statistical Mechanics: Theory
and Experiment. IOP Publishing. https://doi.org/10.1088/1742-5468/abc7c7'
chicago: 'De Nicola, Stefano. “Disentanglement Approach to Quantum Spin Ground States:
Field Theory and Stochastic Simulation.” Journal of Statistical Mechanics:
Theory and Experiment. IOP Publishing, 2021. https://doi.org/10.1088/1742-5468/abc7c7.'
ieee: 'S. De Nicola, “Disentanglement approach to quantum spin ground states: Field
theory and stochastic simulation,” Journal of Statistical Mechanics: Theory
and Experiment, vol. 2021, no. 1. IOP Publishing, 2021.'
ista: 'De Nicola S. 2021. Disentanglement approach to quantum spin ground states:
Field theory and stochastic simulation. Journal of Statistical Mechanics: Theory
and Experiment. 2021(1), 013101.'
mla: 'De Nicola, Stefano. “Disentanglement Approach to Quantum Spin Ground States:
Field Theory and Stochastic Simulation.” Journal of Statistical Mechanics:
Theory and Experiment, vol. 2021, no. 1, 013101, IOP Publishing, 2021, doi:10.1088/1742-5468/abc7c7.'
short: 'S. De Nicola, Journal of Statistical Mechanics: Theory and Experiment 2021
(2021).'
date_created: 2021-02-17T17:48:46Z
date_published: 2021-01-05T00:00:00Z
date_updated: 2023-08-07T13:46:28Z
day: '05'
ddc:
- '530'
department:
- _id: MaSe
doi: 10.1088/1742-5468/abc7c7
ec_funded: 1
external_id:
isi:
- '000605080300001'
file:
- access_level: open_access
checksum: 64e2aae4837790db26e1dd1986c69c07
content_type: application/pdf
creator: dernst
date_created: 2021-02-19T14:04:40Z
date_updated: 2021-02-19T14:04:40Z
file_id: '9172'
file_name: 2021_JourStatMech_deNicola.pdf
file_size: 1693609
relation: main_file
success: 1
file_date_updated: 2021-02-19T14:04:40Z
has_accepted_license: '1'
intvolume: ' 2021'
isi: 1
issue: '1'
keyword:
- Statistics
- Probability and Uncertainty
- Statistics and Probability
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: 'Journal of Statistical Mechanics: Theory and Experiment'
publication_identifier:
issn:
- 1742-5468
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
status: public
title: 'Disentanglement approach to quantum spin ground states: Field theory and stochastic
simulation'
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: 2021
year: '2021'
...
---
_id: '8421'
abstract:
- lang: eng
text: 'The classical Birkhoff conjecture claims that the boundary of a strictly
convex integrable billiard table is necessarily an ellipse (or a circle as a special
case). In this article we prove a complete local version of this conjecture: a
small integrable perturbation of an ellipse must be an ellipse. This extends and
completes the result in Avila-De Simoi-Kaloshin, where nearly circular domains
were considered. One of the crucial ideas in the proof is to extend action-angle
coordinates for elliptic billiards into complex domains (with respect to the angle),
and to thoroughly analyze the nature of their complex singularities. As an application,
we are able to prove some spectral rigidity results for elliptic domains.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Alfonso
full_name: Sorrentino, Alfonso
last_name: Sorrentino
citation:
ama: Kaloshin V, Sorrentino A. On the local Birkhoff conjecture for convex billiards.
Annals of Mathematics. 2018;188(1):315-380. doi:10.4007/annals.2018.188.1.6
apa: Kaloshin, V., & Sorrentino, A. (2018). On the local Birkhoff conjecture
for convex billiards. Annals of Mathematics. Annals of Mathematics, Princeton
U. https://doi.org/10.4007/annals.2018.188.1.6
chicago: Kaloshin, Vadim, and Alfonso Sorrentino. “On the Local Birkhoff Conjecture
for Convex Billiards.” Annals of Mathematics. Annals of Mathematics, Princeton
U, 2018. https://doi.org/10.4007/annals.2018.188.1.6.
ieee: V. Kaloshin and A. Sorrentino, “On the local Birkhoff conjecture for convex
billiards,” Annals of Mathematics, vol. 188, no. 1. Annals of Mathematics,
Princeton U, pp. 315–380, 2018.
ista: Kaloshin V, Sorrentino A. 2018. On the local Birkhoff conjecture for convex
billiards. Annals of Mathematics. 188(1), 315–380.
mla: Kaloshin, Vadim, and Alfonso Sorrentino. “On the Local Birkhoff Conjecture
for Convex Billiards.” Annals of Mathematics, vol. 188, no. 1, Annals of
Mathematics, Princeton U, 2018, pp. 315–80, doi:10.4007/annals.2018.188.1.6.
short: V. Kaloshin, A. Sorrentino, Annals of Mathematics 188 (2018) 315–380.
date_created: 2020-09-17T10:42:22Z
date_published: 2018-07-01T00:00:00Z
date_updated: 2021-01-12T08:19:10Z
day: '01'
doi: 10.4007/annals.2018.188.1.6
extern: '1'
external_id:
arxiv:
- '1612.09194'
intvolume: ' 188'
issue: '1'
keyword:
- Statistics
- Probability and Uncertainty
- Statistics and Probability
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1612.09194
month: '07'
oa: 1
oa_version: Preprint
page: 315-380
publication: Annals of Mathematics
publication_identifier:
issn:
- 0003-486X
publication_status: published
publisher: Annals of Mathematics, Princeton U
quality_controlled: '1'
status: public
title: On the local Birkhoff conjecture for convex billiards
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 188
year: '2018'
...
---
_id: '8526'
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Kaloshin V. An extension of the Artin-Mazur theorem. The Annals of Mathematics.
1999;150(2):729-741. doi:10.2307/121093
apa: Kaloshin, V. (1999). An extension of the Artin-Mazur theorem. The Annals
of Mathematics. JSTOR. https://doi.org/10.2307/121093
chicago: Kaloshin, Vadim. “An Extension of the Artin-Mazur Theorem.” The Annals
of Mathematics. JSTOR, 1999. https://doi.org/10.2307/121093.
ieee: V. Kaloshin, “An extension of the Artin-Mazur theorem,” The Annals of Mathematics,
vol. 150, no. 2. JSTOR, pp. 729–741, 1999.
ista: Kaloshin V. 1999. An extension of the Artin-Mazur theorem. The Annals of Mathematics.
150(2), 729–741.
mla: Kaloshin, Vadim. “An Extension of the Artin-Mazur Theorem.” The Annals of
Mathematics, vol. 150, no. 2, JSTOR, 1999, pp. 729–41, doi:10.2307/121093.
short: V. Kaloshin, The Annals of Mathematics 150 (1999) 729–741.
date_created: 2020-09-18T10:50:28Z
date_published: 1999-09-01T00:00:00Z
date_updated: 2021-01-12T08:19:53Z
day: '01'
doi: 10.2307/121093
extern: '1'
intvolume: ' 150'
issue: '2'
keyword:
- Statistics
- Probability and Uncertainty
- Statistics and Probability
language:
- iso: eng
month: '09'
oa_version: None
page: 729-741
publication: The Annals of Mathematics
publication_identifier:
issn:
- 0003-486X
publication_status: published
publisher: JSTOR
quality_controlled: '1'
status: public
title: An extension of the Artin-Mazur theorem
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 150
year: '1999'
...