---
_id: '1010'
abstract:
- lang: eng
text: 'We prove a local law in the bulk of the spectrum for random Gram matrices
XX∗, a generalization of sample covariance matrices, where X is a large matrix
with independent, centered entries with arbitrary variances. The limiting eigenvalue
density that generalizes the Marchenko-Pastur law is determined by solving a system
of nonlinear equations. Our entrywise and averaged local laws are on the optimal
scale with the optimal error bounds. They hold both in the square case (hard edge)
and in the properly rectangular case (soft edge). In the latter case we also establish
a macroscopic gap away from zero in the spectrum of XX∗. '
article_number: '25'
article_processing_charge: No
arxiv: 1
author:
- first_name: Johannes
full_name: Alt, Johannes
id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
last_name: Alt
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
citation:
ama: Alt J, Erdös L, Krüger TH. Local law for random Gram matrices. Electronic
Journal of Probability. 2017;22. doi:10.1214/17-EJP42
apa: Alt, J., Erdös, L., & Krüger, T. H. (2017). Local law for random Gram matrices.
Electronic Journal of Probability. Institute of Mathematical Statistics.
https://doi.org/10.1214/17-EJP42
chicago: Alt, Johannes, László Erdös, and Torben H Krüger. “Local Law for Random
Gram Matrices.” Electronic Journal of Probability. Institute of Mathematical
Statistics, 2017. https://doi.org/10.1214/17-EJP42.
ieee: J. Alt, L. Erdös, and T. H. Krüger, “Local law for random Gram matrices,”
Electronic Journal of Probability, vol. 22. Institute of Mathematical Statistics,
2017.
ista: Alt J, Erdös L, Krüger TH. 2017. Local law for random Gram matrices. Electronic
Journal of Probability. 22, 25.
mla: Alt, Johannes, et al. “Local Law for Random Gram Matrices.” Electronic Journal
of Probability, vol. 22, 25, Institute of Mathematical Statistics, 2017, doi:10.1214/17-EJP42.
short: J. Alt, L. Erdös, T.H. Krüger, Electronic Journal of Probability 22 (2017).
date_created: 2018-12-11T11:49:40Z
date_published: 2017-03-08T00:00:00Z
date_updated: 2026-04-08T14:11:36Z
day: '08'
ddc:
- '510'
- '539'
department:
- _id: LaEr
doi: 10.1214/17-EJP42
ec_funded: 1
external_id:
arxiv:
- '1606.07353'
isi:
- '000396611900025'
file:
- access_level: open_access
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:13:39Z
date_updated: 2018-12-12T10:13:39Z
file_id: '5024'
file_name: IST-2017-807-v1+1_euclid.ejp.1488942016.pdf
file_size: 639384
relation: main_file
file_date_updated: 2018-12-12T10:13:39Z
has_accepted_license: '1'
intvolume: ' 22'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Electronic Journal of Probability
publication_identifier:
issn:
- 1083-6489
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '6386'
pubrep_id: '807'
quality_controlled: '1'
related_material:
record:
- id: '149'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Local law for random Gram 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: 22
year: '2017'
...
---
_id: '1023'
abstract:
- lang: eng
text: We consider products of independent square non-Hermitian random matrices.
More precisely, let X1,…, Xn be independent N × N random matrices with independent
entries (real or complex with independent real and imaginary parts) with zero
mean and variance 1/N. Soshnikov-O’Rourke [19] and Götze-Tikhomirov [15] showed
that the empirical spectral distribution of the product of n random matrices with
iid entries converges to (equation found). We prove that if the entries of the
matrices X1,…, Xn are independent (but not necessarily identically distributed)
and satisfy uniform subexponential decay condition, then in the bulk the convergence
of the ESD of X1,…, Xn to (0.1) holds up to the scale N–1/2+ε.
article_number: '22'
article_processing_charge: No
author:
- first_name: Yuriy
full_name: Nemish, Yuriy
id: 4D902E6A-F248-11E8-B48F-1D18A9856A87
last_name: Nemish
orcid: 0000-0002-7327-856X
citation:
ama: Nemish Y. Local law for the product of independent non-Hermitian random matrices
with independent entries. Electronic Journal of Probability. 2017;22. doi:10.1214/17-EJP38
apa: Nemish, Y. (2017). Local law for the product of independent non-Hermitian random
matrices with independent entries. Electronic Journal of Probability. Institute
of Mathematical Statistics. https://doi.org/10.1214/17-EJP38
chicago: Nemish, Yuriy. “Local Law for the Product of Independent Non-Hermitian
Random Matrices with Independent Entries.” Electronic Journal of Probability.
Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/17-EJP38.
ieee: Y. Nemish, “Local law for the product of independent non-Hermitian random
matrices with independent entries,” Electronic Journal of Probability,
vol. 22. Institute of Mathematical Statistics, 2017.
ista: Nemish Y. 2017. Local law for the product of independent non-Hermitian random
matrices with independent entries. Electronic Journal of Probability. 22, 22.
mla: Nemish, Yuriy. “Local Law for the Product of Independent Non-Hermitian Random
Matrices with Independent Entries.” Electronic Journal of Probability,
vol. 22, 22, Institute of Mathematical Statistics, 2017, doi:10.1214/17-EJP38.
short: Y. Nemish, Electronic Journal of Probability 22 (2017).
date_created: 2018-12-11T11:49:44Z
date_published: 2017-02-06T00:00:00Z
date_updated: 2025-07-10T11:49:47Z
day: '06'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1214/17-EJP38
external_id:
isi:
- '000396611900022'
file:
- access_level: open_access
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:15:29Z
date_updated: 2018-12-12T10:15:29Z
file_id: '5149'
file_name: IST-2017-802-v1+1_euclid.ejp.1487991681.pdf
file_size: 742275
relation: main_file
file_date_updated: 2018-12-12T10:15:29Z
has_accepted_license: '1'
intvolume: ' 22'
isi: 1
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
publication: Electronic Journal of Probability
publication_identifier:
issn:
- 1083-6489
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '6370'
pubrep_id: '802'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local law for the product of independent non-Hermitian random matrices with
independent entries
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: 22
year: '2017'
...
---
_id: '721'
abstract:
- lang: eng
text: 'Let S be a positivity-preserving symmetric linear operator acting on bounded
functions. The nonlinear equation -1/m=z+Sm with a parameter z in the complex
upper half-plane ℍ has a unique solution m with values in ℍ. We show that the
z-dependence of this solution can be represented as the Stieltjes transforms of
a family of probability measures v on ℝ. Under suitable conditions on S, we show
that v has a real analytic density apart from finitely many algebraic singularities
of degree at most 3. Our motivation comes from large random matrices. The solution
m determines the density of eigenvalues of two prominent matrix ensembles: (i)
matrices with centered independent entries whose variances are given by S and
(ii) matrices with correlated entries with a translation-invariant correlation
structure. Our analysis shows that the limiting eigenvalue density has only square
root singularities or cubic root cusps; no other singularities occur.'
article_processing_charge: No
arxiv: 1
author:
- first_name: Oskari H
full_name: Ajanki, Oskari H
id: 36F2FB7E-F248-11E8-B48F-1D18A9856A87
last_name: Ajanki
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
citation:
ama: Ajanki OH, Krüger TH, Erdös L. Singularities of solutions to quadratic vector
equations on the complex upper half plane. Communications on Pure and Applied
Mathematics. 2017;70(9):1672-1705. doi:10.1002/cpa.21639
apa: Ajanki, O. H., Krüger, T. H., & Erdös, L. (2017). Singularities of solutions
to quadratic vector equations on the complex upper half plane. Communications
on Pure and Applied Mathematics. Wiley. https://doi.org/10.1002/cpa.21639
chicago: Ajanki, Oskari H, Torben H Krüger, and László Erdös. “Singularities of
Solutions to Quadratic Vector Equations on the Complex Upper Half Plane.” Communications
on Pure and Applied Mathematics. Wiley, 2017. https://doi.org/10.1002/cpa.21639.
ieee: O. H. Ajanki, T. H. Krüger, and L. Erdös, “Singularities of solutions to quadratic
vector equations on the complex upper half plane,” Communications on Pure and
Applied Mathematics, vol. 70, no. 9. Wiley, pp. 1672–1705, 2017.
ista: Ajanki OH, Krüger TH, Erdös L. 2017. Singularities of solutions to quadratic
vector equations on the complex upper half plane. Communications on Pure and Applied
Mathematics. 70(9), 1672–1705.
mla: Ajanki, Oskari H., et al. “Singularities of Solutions to Quadratic Vector Equations
on the Complex Upper Half Plane.” Communications on Pure and Applied Mathematics,
vol. 70, no. 9, Wiley, 2017, pp. 1672–705, doi:10.1002/cpa.21639.
short: O.H. Ajanki, T.H. Krüger, L. Erdös, Communications on Pure and Applied Mathematics
70 (2017) 1672–1705.
corr_author: '1'
date_created: 2018-12-11T11:48:08Z
date_published: 2017-09-01T00:00:00Z
date_updated: 2025-09-10T10:58:02Z
day: '01'
department:
- _id: LaEr
doi: 10.1002/cpa.21639
ec_funded: 1
external_id:
arxiv:
- '1512.03703'
isi:
- '000405752100002'
intvolume: ' 70'
isi: 1
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1512.03703
month: '09'
oa: 1
oa_version: Submitted Version
page: 1672 - 1705
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Communications on Pure and Applied Mathematics
publication_identifier:
issn:
- 0010-3640
publication_status: published
publisher: Wiley
publist_id: '6959'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Singularities of solutions to quadratic vector equations on the complex upper
half plane
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 70
year: '2017'
...
---
_id: '733'
abstract:
- lang: eng
text: Let A and B be two N by N deterministic Hermitian matrices and let U be an
N by N Haar distributed unitary matrix. It is well known that the spectral distribution
of the sum H = A + UBU∗ converges weakly to the free additive convolution of the
spectral distributions of A and B, as N tends to infinity. We establish the optimal
convergence rate in the bulk of the spectrum.
acknowledgement: Partially supported by ERC Advanced Grant RANMAT No. 338804, Hong
Kong RGC grant ECS 26301517, and the Göran Gustafsson Foundation
article_processing_charge: No
arxiv: 1
author:
- first_name: Zhigang
full_name: Bao, Zhigang
id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
last_name: Bao
orcid: 0000-0003-3036-1475
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Kevin
full_name: Schnelli, Kevin
id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
last_name: Schnelli
orcid: 0000-0003-0954-3231
citation:
ama: Bao Z, Erdös L, Schnelli K. Convergence rate for spectral distribution of addition
of random matrices. Advances in Mathematics. 2017;319:251-291. doi:10.1016/j.aim.2017.08.028
apa: Bao, Z., Erdös, L., & Schnelli, K. (2017). Convergence rate for spectral
distribution of addition of random matrices. Advances in Mathematics. Academic
Press. https://doi.org/10.1016/j.aim.2017.08.028
chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Convergence Rate for Spectral
Distribution of Addition of Random Matrices.” Advances in Mathematics.
Academic Press, 2017. https://doi.org/10.1016/j.aim.2017.08.028.
ieee: Z. Bao, L. Erdös, and K. Schnelli, “Convergence rate for spectral distribution
of addition of random matrices,” Advances in Mathematics, vol. 319. Academic
Press, pp. 251–291, 2017.
ista: Bao Z, Erdös L, Schnelli K. 2017. Convergence rate for spectral distribution
of addition of random matrices. Advances in Mathematics. 319, 251–291.
mla: Bao, Zhigang, et al. “Convergence Rate for Spectral Distribution of Addition
of Random Matrices.” Advances in Mathematics, vol. 319, Academic Press,
2017, pp. 251–91, doi:10.1016/j.aim.2017.08.028.
short: Z. Bao, L. Erdös, K. Schnelli, Advances in Mathematics 319 (2017) 251–291.
corr_author: '1'
date_created: 2018-12-11T11:48:13Z
date_published: 2017-10-15T00:00:00Z
date_updated: 2025-06-04T10:13:45Z
day: '15'
department:
- _id: LaEr
doi: 10.1016/j.aim.2017.08.028
ec_funded: 1
external_id:
arxiv:
- '1606.03076'
isi:
- '000412150400010'
intvolume: ' 319'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1606.03076
month: '10'
oa: 1
oa_version: Submitted Version
page: 251 - 291
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Advances in Mathematics
publication_status: published
publisher: Academic Press
publist_id: '6935'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Convergence rate for spectral distribution of addition of random matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 319
year: '2017'
...
---
_id: '1157'
abstract:
- lang: eng
text: We consider sample covariance matrices of the form Q = ( σ1/2X)(σ1/2X)∗, where
the sample X is an M ×N random matrix whose entries are real independent random
variables with variance 1/N and whereσ is an M × M positive-definite deterministic
matrix. We analyze the asymptotic fluctuations of the largest rescaled eigenvalue
of Q when both M and N tend to infinity with N/M →d ϵ (0,∞). For a large class
of populations σ in the sub-critical regime, we show that the distribution of
the largest rescaled eigenvalue of Q is given by the type-1 Tracy-Widom distribution
under the additional assumptions that (1) either the entries of X are i.i.d. Gaussians
or (2) that σ is diagonal and that the entries of X have a sub-exponential decay.
acknowledgement: "We thank Horng-Tzer Yau for numerous discussions and remarks. We
are grateful to Ben Adlam, Jinho Baik, Zhigang Bao, Paul Bourgade, László Erd ̋os,
Iain Johnstone and Antti Knowles for comments. We are also grate-\r\nful to the
anonymous referee for carefully reading our manuscript and suggesting several improvements."
article_processing_charge: No
arxiv: 1
author:
- first_name: Ji
full_name: Lee, Ji
last_name: Lee
- first_name: Kevin
full_name: Schnelli, Kevin
id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
last_name: Schnelli
orcid: 0000-0003-0954-3231
citation:
ama: Lee J, Schnelli K. Tracy-widom distribution for the largest eigenvalue of real
sample covariance matrices with general population. Annals of Applied Probability.
2016;26(6):3786-3839. doi:10.1214/16-AAP1193
apa: Lee, J., & Schnelli, K. (2016). Tracy-widom distribution for the largest
eigenvalue of real sample covariance matrices with general population. Annals
of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/16-AAP1193
chicago: Lee, Ji, and Kevin Schnelli. “Tracy-Widom Distribution for the Largest
Eigenvalue of Real Sample Covariance Matrices with General Population.” Annals
of Applied Probability. Institute of Mathematical Statistics, 2016. https://doi.org/10.1214/16-AAP1193.
ieee: J. Lee and K. Schnelli, “Tracy-widom distribution for the largest eigenvalue
of real sample covariance matrices with general population,” Annals of Applied
Probability, vol. 26, no. 6. Institute of Mathematical Statistics, pp. 3786–3839,
2016.
ista: Lee J, Schnelli K. 2016. Tracy-widom distribution for the largest eigenvalue
of real sample covariance matrices with general population. Annals of Applied
Probability. 26(6), 3786–3839.
mla: Lee, Ji, and Kevin Schnelli. “Tracy-Widom Distribution for the Largest Eigenvalue
of Real Sample Covariance Matrices with General Population.” Annals of Applied
Probability, vol. 26, no. 6, Institute of Mathematical Statistics, 2016, pp.
3786–839, doi:10.1214/16-AAP1193.
short: J. Lee, K. Schnelli, Annals of Applied Probability 26 (2016) 3786–3839.
date_created: 2018-12-11T11:50:27Z
date_published: 2016-12-15T00:00:00Z
date_updated: 2025-09-22T09:55:43Z
day: '15'
department:
- _id: LaEr
doi: 10.1214/16-AAP1193
ec_funded: 1
external_id:
arxiv:
- '1409.4979'
isi:
- '000391240100016'
intvolume: ' 26'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1409.4979
month: '12'
oa: 1
oa_version: Preprint
page: 3786 - 3839
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Annals of Applied Probability
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '6201'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Tracy-widom distribution for the largest eigenvalue of real sample covariance
matrices with general population
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 26
year: '2016'
...
---
_id: '1219'
abstract:
- lang: eng
text: We consider N×N random matrices of the form H = W + V where W is a real symmetric
or complex Hermitian Wigner matrix and V is a random or deterministic, real, diagonal
matrix whose entries are independent of W. We assume subexponential decay for
the matrix entries of W, and we choose V so that the eigenvalues ofW and V are
typically of the same order. For a large class of diagonal matrices V , we show
that the local statistics in the bulk of the spectrum are universal in the limit
of large N.
acknowledgement: "J.C. was supported in part by National Research Foundation of Korea
Grant 2011-0013474 and TJ Park Junior Faculty Fellowship.\r\nK.S. was supported
by ERC Advanced Grant RANMAT, No. 338804, and the \"Fund for Math.\"\r\nB.S. was
supported by NSF GRFP Fellowship DGE-1144152.\r\nH.Y. was supported in part by NSF
Grant DMS-13-07444 and Simons investigator fellowship. We thank Paul Bourgade, László
Erd ̋os and Antti Knowles for helpful comments. We are grateful to the Taida Institute
for Mathematical\r\nSciences and National Taiwan Universality for their hospitality
during part of this\r\nresearch. We thank Thomas Spencer and the Institute for Advanced
Study for their\r\nhospitality during the academic year 2013–2014. "
article_processing_charge: No
arxiv: 1
author:
- first_name: Jioon
full_name: Lee, Jioon
last_name: Lee
- first_name: Kevin
full_name: Schnelli, Kevin
id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
last_name: Schnelli
orcid: 0000-0003-0954-3231
- first_name: Ben
full_name: Stetler, Ben
last_name: Stetler
- first_name: Horngtzer
full_name: Yau, Horngtzer
last_name: Yau
citation:
ama: Lee J, Schnelli K, Stetler B, Yau H. Bulk universality for deformed wigner
matrices. Annals of Probability. 2016;44(3):2349-2425. doi:10.1214/15-AOP1023
apa: Lee, J., Schnelli, K., Stetler, B., & Yau, H. (2016). Bulk universality
for deformed wigner matrices. Annals of Probability. Institute of Mathematical
Statistics. https://doi.org/10.1214/15-AOP1023
chicago: Lee, Jioon, Kevin Schnelli, Ben Stetler, and Horngtzer Yau. “Bulk Universality
for Deformed Wigner Matrices.” Annals of Probability. Institute of Mathematical
Statistics, 2016. https://doi.org/10.1214/15-AOP1023.
ieee: J. Lee, K. Schnelli, B. Stetler, and H. Yau, “Bulk universality for deformed
wigner matrices,” Annals of Probability, vol. 44, no. 3. Institute of Mathematical
Statistics, pp. 2349–2425, 2016.
ista: Lee J, Schnelli K, Stetler B, Yau H. 2016. Bulk universality for deformed
wigner matrices. Annals of Probability. 44(3), 2349–2425.
mla: Lee, Jioon, et al. “Bulk Universality for Deformed Wigner Matrices.” Annals
of Probability, vol. 44, no. 3, Institute of Mathematical Statistics, 2016,
pp. 2349–425, doi:10.1214/15-AOP1023.
short: J. Lee, K. Schnelli, B. Stetler, H. Yau, Annals of Probability 44 (2016)
2349–2425.
date_created: 2018-12-11T11:50:47Z
date_published: 2016-01-01T00:00:00Z
date_updated: 2025-09-22T09:33:43Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/15-AOP1023
ec_funded: 1
external_id:
arxiv:
- '1405.6634'
isi:
- '000376180700016'
intvolume: ' 44'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1405.6634
month: '01'
oa: 1
oa_version: Preprint
page: 2349 - 2425
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Annals of Probability
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '6115'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bulk universality for deformed wigner matrices
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 44
year: '2016'
...
---
_id: '1223'
abstract:
- lang: eng
text: We consider a random Schrödinger operator on the binary tree with a random
potential which is the sum of a random radially symmetric potential, Qr, and a
random transversally periodic potential, κQt, with coupling constant κ. Using
a new one-dimensional dynamical systems approach combined with Jensen's inequality
in hyperbolic space (our key estimate) we obtain a fractional moment estimate
proving localization for small and large κ. Together with a previous result we
therefore obtain a model with two Anderson transitions, from localization to delocalization
and back to localization, when increasing κ. As a by-product we also have a partially
new proof of one-dimensional Anderson localization at any disorder.
article_processing_charge: No
arxiv: 1
author:
- first_name: Richard
full_name: Froese, Richard
last_name: Froese
- first_name: Darrick
full_name: Lee, Darrick
last_name: Lee
- first_name: Christian
full_name: Sadel, Christian
id: 4760E9F8-F248-11E8-B48F-1D18A9856A87
last_name: Sadel
orcid: 0000-0001-8255-3968
- first_name: Wolfgang
full_name: Spitzer, Wolfgang
last_name: Spitzer
- first_name: Günter
full_name: Stolz, Günter
last_name: Stolz
citation:
ama: Froese R, Lee D, Sadel C, Spitzer W, Stolz G. Localization for transversally
periodic random potentials on binary trees. Journal of Spectral Theory.
2016;6(3):557-600. doi:10.4171/JST/132
apa: Froese, R., Lee, D., Sadel, C., Spitzer, W., & Stolz, G. (2016). Localization
for transversally periodic random potentials on binary trees. Journal of Spectral
Theory. European Mathematical Society. https://doi.org/10.4171/JST/132
chicago: Froese, Richard, Darrick Lee, Christian Sadel, Wolfgang Spitzer, and Günter
Stolz. “Localization for Transversally Periodic Random Potentials on Binary Trees.”
Journal of Spectral Theory. European Mathematical Society, 2016. https://doi.org/10.4171/JST/132.
ieee: R. Froese, D. Lee, C. Sadel, W. Spitzer, and G. Stolz, “Localization for transversally
periodic random potentials on binary trees,” Journal of Spectral Theory,
vol. 6, no. 3. European Mathematical Society, pp. 557–600, 2016.
ista: Froese R, Lee D, Sadel C, Spitzer W, Stolz G. 2016. Localization for transversally
periodic random potentials on binary trees. Journal of Spectral Theory. 6(3),
557–600.
mla: Froese, Richard, et al. “Localization for Transversally Periodic Random Potentials
on Binary Trees.” Journal of Spectral Theory, vol. 6, no. 3, European Mathematical
Society, 2016, pp. 557–600, doi:10.4171/JST/132.
short: R. Froese, D. Lee, C. Sadel, W. Spitzer, G. Stolz, Journal of Spectral Theory
6 (2016) 557–600.
date_created: 2018-12-11T11:50:48Z
date_published: 2016-01-01T00:00:00Z
date_updated: 2025-09-22T09:32:55Z
day: '01'
department:
- _id: LaEr
doi: 10.4171/JST/132
external_id:
arxiv:
- '1408.3961'
isi:
- '000388627000004'
intvolume: ' 6'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1408.3961
month: '01'
oa: 1
oa_version: Preprint
page: 557 - 600
publication: Journal of Spectral Theory
publication_status: published
publisher: European Mathematical Society
publist_id: '6112'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Localization for transversally periodic random potentials on binary trees
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 6
year: '2016'
...
---
_id: '1257'
abstract:
- lang: eng
text: We consider products of random matrices that are small, independent identically
distributed perturbations of a fixed matrix (Formula presented.). Focusing on
the eigenvalues of (Formula presented.) of a particular size we obtain a limit
to a SDE in a critical scaling. Previous results required (Formula presented.)
to be a (conjugated) unitary matrix so it could not have eigenvalues of different
modulus. From the result we can also obtain a limit SDE for the Markov process
given by the action of the random products on the flag manifold. Applying the
result to random Schrödinger operators we can improve some results by Valko and
Virag showing GOE statistics for the rescaled eigenvalue process of a sequence
of Anderson models on long boxes. In particular, we solve a problem posed in their
work.
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). The work of C. Sadel was supported by NSERC Discovery Grant 92997-2010
RGPIN and by the People Programme (Marie Curie Actions) of the EU 7th Framework
Programme FP7/2007-2013, REA Grant 291734.
article_processing_charge: Yes (via OA deal)
author:
- first_name: Christian
full_name: Sadel, Christian
id: 4760E9F8-F248-11E8-B48F-1D18A9856A87
last_name: Sadel
orcid: 0000-0001-8255-3968
- first_name: Bálint
full_name: Virág, Bálint
last_name: Virág
citation:
ama: Sadel C, Virág B. A central limit theorem for products of random matrices and
GOE statistics for the Anderson model on long boxes. Communications in Mathematical
Physics. 2016;343(3):881-919. doi:10.1007/s00220-016-2600-4
apa: Sadel, C., & Virág, B. (2016). A central limit theorem for products of
random matrices and GOE statistics for the Anderson model on long boxes. Communications
in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-016-2600-4
chicago: Sadel, Christian, and Bálint Virág. “A Central Limit Theorem for Products
of Random Matrices and GOE Statistics for the Anderson Model on Long Boxes.” Communications
in Mathematical Physics. Springer, 2016. https://doi.org/10.1007/s00220-016-2600-4.
ieee: C. Sadel and B. Virág, “A central limit theorem for products of random matrices
and GOE statistics for the Anderson model on long boxes,” Communications in
Mathematical Physics, vol. 343, no. 3. Springer, pp. 881–919, 2016.
ista: Sadel C, Virág B. 2016. A central limit theorem for products of random matrices
and GOE statistics for the Anderson model on long boxes. Communications in Mathematical
Physics. 343(3), 881–919.
mla: Sadel, Christian, and Bálint Virág. “A Central Limit Theorem for Products of
Random Matrices and GOE Statistics for the Anderson Model on Long Boxes.” Communications
in Mathematical Physics, vol. 343, no. 3, Springer, 2016, pp. 881–919, doi:10.1007/s00220-016-2600-4.
short: C. Sadel, B. Virág, Communications in Mathematical Physics 343 (2016) 881–919.
corr_author: '1'
date_created: 2018-12-11T11:50:59Z
date_published: 2016-05-01T00:00:00Z
date_updated: 2025-09-22T09:02:32Z
day: '01'
ddc:
- '510'
- '539'
department:
- _id: LaEr
doi: 10.1007/s00220-016-2600-4
ec_funded: 1
external_id:
isi:
- '000374659800005'
file:
- access_level: open_access
checksum: 4fb2411d9c2f56676123165aad46c828
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:15:02Z
date_updated: 2020-07-14T12:44:42Z
file_id: '5119'
file_name: IST-2016-703-v1+1_s00220-016-2600-4.pdf
file_size: 800792
relation: main_file
file_date_updated: 2020-07-14T12:44:42Z
has_accepted_license: '1'
intvolume: ' 343'
isi: 1
issue: '3'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 881 - 919
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '6067'
pubrep_id: '703'
quality_controlled: '1'
scopus_import: '1'
status: public
title: A central limit theorem for products of random matrices and GOE statistics
for the Anderson model on long boxes
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 343
year: '2016'
...
---
_id: '1280'
abstract:
- lang: eng
text: We prove the Wigner-Dyson-Mehta conjecture at fixed energy in the bulk of
the spectrum for generalized symmetric and Hermitian Wigner matrices. Previous
results concerning the universality of random matrices either require an averaging
in the energy parameter or they hold only for Hermitian matrices if the energy
parameter is fixed. We develop a homogenization theory of the Dyson Brownian motion
and show that microscopic universality follows from mesoscopic statistics.
acknowledgement: "The work of P.B. was partially supported by National Sci-\r\nence
Foundation Grant DMS-1208859. The work of L.E. was partially supported\r\nby ERC
Advanced Grant RANMAT 338804. The work of H.-T. Y. was partially\r\nsupported by
National Science Foundation Grant DMS-1307444 and a Simons In-\r\nvestigator award.
\ The work of J.Y. was partially supported by National Science\r\nFoundation Grant
DMS-1207961. The major part of this research was conducted\r\nwhen all authors
were visiting IAS and were also supported by National Science\r\nFoundation Grant
DMS-1128255."
article_processing_charge: No
arxiv: 1
author:
- first_name: Paul
full_name: Bourgade, Paul
last_name: Bourgade
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Horngtzer
full_name: Yau, Horngtzer
last_name: Yau
- first_name: Jun
full_name: Yin, Jun
last_name: Yin
citation:
ama: Bourgade P, Erdös L, Yau H, Yin J. Fixed energy universality for generalized
wigner matrices. Communications on Pure and Applied Mathematics. 2016;69(10):1815-1881.
doi:10.1002/cpa.21624
apa: Bourgade, P., Erdös, L., Yau, H., & Yin, J. (2016). Fixed energy universality
for generalized wigner matrices. Communications on Pure and Applied Mathematics.
Wiley-Blackwell. https://doi.org/10.1002/cpa.21624
chicago: Bourgade, Paul, László Erdös, Horngtzer Yau, and Jun Yin. “Fixed Energy
Universality for Generalized Wigner Matrices.” Communications on Pure and Applied
Mathematics. Wiley-Blackwell, 2016. https://doi.org/10.1002/cpa.21624.
ieee: P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Fixed energy universality for
generalized wigner matrices,” Communications on Pure and Applied Mathematics,
vol. 69, no. 10. Wiley-Blackwell, pp. 1815–1881, 2016.
ista: Bourgade P, Erdös L, Yau H, Yin J. 2016. Fixed energy universality for generalized
wigner matrices. Communications on Pure and Applied Mathematics. 69(10), 1815–1881.
mla: Bourgade, Paul, et al. “Fixed Energy Universality for Generalized Wigner Matrices.”
Communications on Pure and Applied Mathematics, vol. 69, no. 10, Wiley-Blackwell,
2016, pp. 1815–81, doi:10.1002/cpa.21624.
short: P. Bourgade, L. Erdös, H. Yau, J. Yin, Communications on Pure and Applied
Mathematics 69 (2016) 1815–1881.
corr_author: '1'
date_created: 2018-12-11T11:51:07Z
date_published: 2016-10-01T00:00:00Z
date_updated: 2025-09-22T08:35:52Z
day: '01'
department:
- _id: LaEr
doi: 10.1002/cpa.21624
ec_funded: 1
external_id:
arxiv:
- '1407.5606'
isi:
- '000382932900001'
intvolume: ' 69'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1407.5606
month: '10'
oa: 1
oa_version: Preprint
page: 1815 - 1881
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Communications on Pure and Applied Mathematics
publication_status: published
publisher: Wiley-Blackwell
publist_id: '6036'
scopus_import: '1'
status: public
title: Fixed energy universality for generalized wigner matrices
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 69
year: '2016'
...
---
_id: '1434'
abstract:
- lang: eng
text: We prove that the system of subordination equations, defining the free additive
convolution of two probability measures, is stable away from the edges of the
support and blow-up singularities by showing that the recent smoothness condition
of Kargin is always satisfied. As an application, we consider the local spectral
statistics of the random matrix ensemble A+UBU⁎A+UBU⁎, where U is a Haar distributed
random unitary or orthogonal matrix, and A and B are deterministic matrices.
In the bulk regime, we prove that the empirical spectral distribution of A+UBU⁎A+UBU⁎
concentrates around the free additive convolution of the spectral distributions
of A and B on scales down to N−2/3N−2/3.
article_processing_charge: No
arxiv: 1
author:
- first_name: Zhigang
full_name: Bao, Zhigang
id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
last_name: Bao
orcid: 0000-0003-3036-1475
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Kevin
full_name: Schnelli, Kevin
id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
last_name: Schnelli
orcid: 0000-0003-0954-3231
citation:
ama: Bao Z, Erdös L, Schnelli K. Local stability of the free additive convolution.
Journal of Functional Analysis. 2016;271(3):672-719. doi:10.1016/j.jfa.2016.04.006
apa: Bao, Z., Erdös, L., & Schnelli, K. (2016). Local stability of the free
additive convolution. Journal of Functional Analysis. Academic Press. https://doi.org/10.1016/j.jfa.2016.04.006
chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Stability of the
Free Additive Convolution.” Journal of Functional Analysis. Academic Press,
2016. https://doi.org/10.1016/j.jfa.2016.04.006.
ieee: Z. Bao, L. Erdös, and K. Schnelli, “Local stability of the free additive convolution,”
Journal of Functional Analysis, vol. 271, no. 3. Academic Press, pp. 672–719,
2016.
ista: Bao Z, Erdös L, Schnelli K. 2016. Local stability of the free additive convolution.
Journal of Functional Analysis. 271(3), 672–719.
mla: Bao, Zhigang, et al. “Local Stability of the Free Additive Convolution.” Journal
of Functional Analysis, vol. 271, no. 3, Academic Press, 2016, pp. 672–719,
doi:10.1016/j.jfa.2016.04.006.
short: Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 271 (2016)
672–719.
corr_author: '1'
date_created: 2018-12-11T11:52:00Z
date_published: 2016-08-01T00:00:00Z
date_updated: 2025-09-18T14:00:03Z
day: '01'
department:
- _id: LaEr
doi: 10.1016/j.jfa.2016.04.006
ec_funded: 1
external_id:
arxiv:
- '1508.05905'
isi:
- '000378013400009'
intvolume: ' 271'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1508.05905
month: '08'
oa: 1
oa_version: Preprint
page: 672 - 719
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Journal of Functional Analysis
publication_status: published
publisher: Academic Press
publist_id: '5764'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local stability of the free additive convolution
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 271
year: '2016'
...
---
_id: '1489'
abstract:
- lang: eng
text: 'We prove optimal local law, bulk universality and non-trivial decay for the
off-diagonal elements of the resolvent for a class of translation invariant Gaussian
random matrix ensembles with correlated entries. '
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). Oskari H. Ajanki was Partially supported by ERC Advanced Grant RANMAT
No. 338804, and SFB-TR 12 Grant of the German Research Council. László Erdős was
Partially supported by ERC Advanced Grant RANMAT No. 338804. Torben Krüger was Partially
supported by ERC Advanced Grant RANMAT No. 338804, and SFB-TR 12 Grant of the German
Research Council.
article_processing_charge: Yes (via OA deal)
author:
- first_name: Oskari H
full_name: Ajanki, Oskari H
id: 36F2FB7E-F248-11E8-B48F-1D18A9856A87
last_name: Ajanki
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
citation:
ama: Ajanki OH, Erdös L, Krüger TH. Local spectral statistics of Gaussian matrices
with correlated entries. Journal of Statistical Physics. 2016;163(2):280-302.
doi:10.1007/s10955-016-1479-y
apa: Ajanki, O. H., Erdös, L., & Krüger, T. H. (2016). Local spectral statistics
of Gaussian matrices with correlated entries. Journal of Statistical Physics.
Springer. https://doi.org/10.1007/s10955-016-1479-y
chicago: Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Local Spectral Statistics
of Gaussian Matrices with Correlated Entries.” Journal of Statistical Physics.
Springer, 2016. https://doi.org/10.1007/s10955-016-1479-y.
ieee: O. H. Ajanki, L. Erdös, and T. H. Krüger, “Local spectral statistics of Gaussian
matrices with correlated entries,” Journal of Statistical Physics, vol.
163, no. 2. Springer, pp. 280–302, 2016.
ista: Ajanki OH, Erdös L, Krüger TH. 2016. Local spectral statistics of Gaussian
matrices with correlated entries. Journal of Statistical Physics. 163(2), 280–302.
mla: Ajanki, Oskari H., et al. “Local Spectral Statistics of Gaussian Matrices with
Correlated Entries.” Journal of Statistical Physics, vol. 163, no. 2, Springer,
2016, pp. 280–302, doi:10.1007/s10955-016-1479-y.
short: O.H. Ajanki, L. Erdös, T.H. Krüger, Journal of Statistical Physics 163 (2016)
280–302.
corr_author: '1'
date_created: 2018-12-11T11:52:19Z
date_published: 2016-04-01T00:00:00Z
date_updated: 2025-09-18T11:17:50Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s10955-016-1479-y
ec_funded: 1
external_id:
isi:
- '000373132700003'
file:
- access_level: open_access
checksum: 7139598dcb1cafbe6866bd2bfd732b33
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:11:16Z
date_updated: 2020-07-14T12:44:57Z
file_id: '4869'
file_name: IST-2016-516-v1+1_s10955-016-1479-y.pdf
file_size: 660602
relation: main_file
file_date_updated: 2020-07-14T12:44:57Z
has_accepted_license: '1'
intvolume: ' 163'
isi: 1
issue: '2'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 280 - 302
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Journal of Statistical Physics
publication_status: published
publisher: Springer
publist_id: '5698'
pubrep_id: '516'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local spectral statistics of Gaussian matrices with correlated entries
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 163
year: '2016'
...
---
_id: '1608'
abstract:
- lang: eng
text: 'We show that the Anderson model has a transition from localization to delocalization
at exactly 2 dimensional growth rate on antitrees with normalized edge weights
which are certain discrete graphs. The kinetic part has a one-dimensional structure
allowing a description through transfer matrices which involve some Schur complement.
For such operators we introduce the notion of having one propagating channel and
extend theorems from the theory of one-dimensional Jacobi operators that relate
the behavior of transfer matrices with the spectrum. These theorems are then applied
to the considered model. In essence, in a certain energy region the kinetic part
averages the random potentials along shells and the transfer matrices behave similar
as for a one-dimensional operator with random potential of decaying variance.
At d dimensional growth for d>2 this effective decay is strong enough to obtain
absolutely continuous spectrum, whereas for some uniform d dimensional growth
with d<2 one has pure point spectrum in this energy region. At exactly uniform
2 dimensional growth also some singular continuous spectrum appears, at least
at small disorder. As a corollary we also obtain a change from singular spectrum
(d≤2) to absolutely continuous spectrum (d≥3) for random operators of the type
rΔdr+λ on ℤd, where r is an orthogonal radial projection, Δd the discrete
adjacency operator (Laplacian) on ℤd and λ a random potential. '
article_processing_charge: No
arxiv: 1
author:
- first_name: Christian
full_name: Sadel, Christian
id: 4760E9F8-F248-11E8-B48F-1D18A9856A87
last_name: Sadel
orcid: 0000-0001-8255-3968
citation:
ama: Sadel C. Anderson transition at 2 dimensional growth rate on antitrees and
spectral theory for operators with one propagating channel. Annales Henri Poincare.
2016;17(7):1631-1675. doi:10.1007/s00023-015-0456-3
apa: Sadel, C. (2016). Anderson transition at 2 dimensional growth rate on antitrees
and spectral theory for operators with one propagating channel. Annales Henri
Poincare. Birkhäuser. https://doi.org/10.1007/s00023-015-0456-3
chicago: Sadel, Christian. “Anderson Transition at 2 Dimensional Growth Rate on
Antitrees and Spectral Theory for Operators with One Propagating Channel.” Annales
Henri Poincare. Birkhäuser, 2016. https://doi.org/10.1007/s00023-015-0456-3.
ieee: C. Sadel, “Anderson transition at 2 dimensional growth rate on antitrees and
spectral theory for operators with one propagating channel,” Annales Henri
Poincare, vol. 17, no. 7. Birkhäuser, pp. 1631–1675, 2016.
ista: Sadel C. 2016. Anderson transition at 2 dimensional growth rate on antitrees
and spectral theory for operators with one propagating channel. Annales Henri
Poincare. 17(7), 1631–1675.
mla: Sadel, Christian. “Anderson Transition at 2 Dimensional Growth Rate on Antitrees
and Spectral Theory for Operators with One Propagating Channel.” Annales Henri
Poincare, vol. 17, no. 7, Birkhäuser, 2016, pp. 1631–75, doi:10.1007/s00023-015-0456-3.
short: C. Sadel, Annales Henri Poincare 17 (2016) 1631–1675.
corr_author: '1'
date_created: 2018-12-11T11:53:00Z
date_published: 2016-07-01T00:00:00Z
date_updated: 2025-09-18T11:00:43Z
day: '01'
department:
- _id: LaEr
doi: 10.1007/s00023-015-0456-3
ec_funded: 1
external_id:
arxiv:
- '1501.04287'
isi:
- '000377994000003'
intvolume: ' 17'
isi: 1
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1501.04287
month: '07'
oa: 1
oa_version: Preprint
page: 1631 - 1675
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Annales Henri Poincare
publication_status: published
publisher: Birkhäuser
publist_id: '5558'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Anderson transition at 2 dimensional growth rate on antitrees and spectral
theory for operators with one propagating channel
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 17
year: '2016'
...
---
_id: '1881'
abstract:
- lang: eng
text: 'We consider random matrices of the form H=W+λV, λ∈ℝ+, where W is a real symmetric
or complex Hermitian Wigner matrix of size N and V is a real bounded diagonal
random matrix of size N with i.i.d.\ entries that are independent of W. We assume
subexponential decay for the matrix entries of W and we choose λ∼1, so that the
eigenvalues of W and λV are typically of the same order. Further, we assume that
the density of the entries of V is supported on a single interval and is convex
near the edges of its support. In this paper we prove that there is λ+∈ℝ+ such
that the largest eigenvalues of H are in the limit of large N determined by the
order statistics of V for λ>λ+. In particular, the largest eigenvalue of H
has a Weibull distribution in the limit N→∞ if λ>λ+. Moreover, for N sufficiently
large, we show that the eigenvectors associated to the largest eigenvalues are
partially localized for λ>λ+, while they are completely delocalized for λ<λ+.
Similar results hold for the lowest eigenvalues. '
acknowledgement: "Most of the presented work was obtained while Kevin Schnelli was
staying at the IAS with the support of\r\nThe Fund For Math."
article_processing_charge: No
arxiv: 1
author:
- first_name: Jioon
full_name: Lee, Jioon
last_name: Lee
- first_name: Kevin
full_name: Schnelli, Kevin
id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
last_name: Schnelli
orcid: 0000-0003-0954-3231
citation:
ama: Lee J, Schnelli K. Extremal eigenvalues and eigenvectors of deformed Wigner
matrices. Probability Theory and Related Fields. 2016;164(1-2):165-241.
doi:10.1007/s00440-014-0610-8
apa: Lee, J., & Schnelli, K. (2016). Extremal eigenvalues and eigenvectors of
deformed Wigner matrices. Probability Theory and Related Fields. Springer.
https://doi.org/10.1007/s00440-014-0610-8
chicago: Lee, Jioon, and Kevin Schnelli. “Extremal Eigenvalues and Eigenvectors
of Deformed Wigner Matrices.” Probability Theory and Related Fields. Springer,
2016. https://doi.org/10.1007/s00440-014-0610-8.
ieee: J. Lee and K. Schnelli, “Extremal eigenvalues and eigenvectors of deformed
Wigner matrices,” Probability Theory and Related Fields, vol. 164, no.
1–2. Springer, pp. 165–241, 2016.
ista: Lee J, Schnelli K. 2016. Extremal eigenvalues and eigenvectors of deformed
Wigner matrices. Probability Theory and Related Fields. 164(1–2), 165–241.
mla: Lee, Jioon, and Kevin Schnelli. “Extremal Eigenvalues and Eigenvectors of Deformed
Wigner Matrices.” Probability Theory and Related Fields, vol. 164, no.
1–2, Springer, 2016, pp. 165–241, doi:10.1007/s00440-014-0610-8.
short: J. Lee, K. Schnelli, Probability Theory and Related Fields 164 (2016) 165–241.
corr_author: '1'
date_created: 2018-12-11T11:54:31Z
date_published: 2016-02-01T00:00:00Z
date_updated: 2025-09-18T10:46:46Z
day: '01'
department:
- _id: LaEr
doi: 10.1007/s00440-014-0610-8
ec_funded: 1
external_id:
arxiv:
- '1310.7057'
isi:
- '000373163300006'
intvolume: ' 164'
isi: 1
issue: 1-2
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1310.7057
month: '02'
oa: 1
oa_version: Preprint
page: 165 - 241
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Probability Theory and Related Fields
publication_status: published
publisher: Springer
publist_id: '5215'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Extremal eigenvalues and eigenvectors of deformed Wigner matrices
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 164
year: '2016'
...
---
_id: '2166'
abstract:
- lang: eng
text: 'We consider the spectral statistics of large random band matrices on mesoscopic
energy scales. We show that the correlation function of the local eigenvalue density
exhibits a universal power law behaviour that differs from the Wigner-Dyson- Mehta
statistics. This law had been predicted in the physics literature by Altshuler
and Shklovskii in (Zh Eksp Teor Fiz (Sov Phys JETP) 91(64):220(127), 1986); it
describes the correlations of the eigenvalue density in general metallic sampleswith
weak disorder. Our result rigorously establishes the Altshuler-Shklovskii formulas
for band matrices. In two dimensions, where the leading term vanishes owing to
an algebraic cancellation, we identify the first non-vanishing term and show that
it differs substantially from the prediction of Kravtsov and Lerner in (Phys Rev
Lett 74:2563-2566, 1995). The proof is given in the current paper and its companion
(Ann. H. Poincaré. arXiv:1309.5107, 2014). '
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: Antti
full_name: Knowles, Antti
last_name: Knowles
citation:
ama: 'Erdös L, Knowles A. The Altshuler-Shklovskii formulas for random band matrices
I: the unimodular case. Communications in Mathematical Physics. 2015;333(3):1365-1416.
doi:10.1007/s00220-014-2119-5'
apa: 'Erdös, L., & Knowles, A. (2015). The Altshuler-Shklovskii formulas for
random band matrices I: the unimodular case. Communications in Mathematical
Physics. Springer. https://doi.org/10.1007/s00220-014-2119-5'
chicago: 'Erdös, László, and Antti Knowles. “The Altshuler-Shklovskii Formulas for
Random Band Matrices I: The Unimodular Case.” Communications in Mathematical
Physics. Springer, 2015. https://doi.org/10.1007/s00220-014-2119-5.'
ieee: 'L. Erdös and A. Knowles, “The Altshuler-Shklovskii formulas for random band
matrices I: the unimodular case,” Communications in Mathematical Physics,
vol. 333, no. 3. Springer, pp. 1365–1416, 2015.'
ista: 'Erdös L, Knowles A. 2015. The Altshuler-Shklovskii formulas for random band
matrices I: the unimodular case. Communications in Mathematical Physics. 333(3),
1365–1416.'
mla: 'Erdös, László, and Antti Knowles. “The Altshuler-Shklovskii Formulas for Random
Band Matrices I: The Unimodular Case.” Communications in Mathematical Physics,
vol. 333, no. 3, Springer, 2015, pp. 1365–416, doi:10.1007/s00220-014-2119-5.'
short: L. Erdös, A. Knowles, Communications in Mathematical Physics 333 (2015) 1365–1416.
date_created: 2018-12-11T11:56:05Z
date_published: 2015-02-01T00:00:00Z
date_updated: 2025-09-23T13:39:37Z
day: '01'
department:
- _id: LaEr
doi: 10.1007/s00220-014-2119-5
external_id:
arxiv:
- '1309.5106'
isi:
- '000348303100008'
intvolume: ' 333'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1309.5106
month: '02'
oa: 1
oa_version: Preprint
page: 1365 - 1416
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4818'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'The Altshuler-Shklovskii formulas for random band matrices I: the unimodular
case'
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 333
year: '2015'
...
---
_id: '1505'
abstract:
- lang: eng
text: This paper is aimed at deriving the universality of the largest eigenvalue
of a class of high-dimensional real or complex sample covariance matrices of the
form W N =Σ 1/2XX∗Σ 1/2 . Here, X = (xij )M,N is an M× N random matrix with independent
entries xij , 1 ≤ i M,≤ 1 ≤ j ≤ N such that Exij = 0, E|xij |2 = 1/N . On dimensionality,
we assume that M = M(N) and N/M → d ε (0, ∞) as N ∞→. For a class of general deterministic
positive-definite M × M matrices Σ , under some additional assumptions on the
distribution of xij 's, we show that the limiting behavior of the largest eigenvalue
of W N is universal, via pursuing a Green function comparison strategy raised
in [Probab. Theory Related Fields 154 (2012) 341-407, Adv. Math. 229 (2012) 1435-1515]
by Erd″os, Yau and Yin for Wigner matrices and extended by Pillai and Yin [Ann.
Appl. Probab. 24 (2014) 935-1001] to sample covariance matrices in the null case
(&Epsi = I ). Consequently, in the standard complex case (Ex2 ij = 0), combing
this universality property and the results known for Gaussian matrices obtained
by El Karoui in [Ann. Probab. 35 (2007) 663-714] (nonsingular case) and Onatski
in [Ann. Appl. Probab. 18 (2008) 470-490] (singular case), we show that after
an appropriate normalization the largest eigenvalue of W N converges weakly to
the type 2 Tracy-Widom distribution TW2 . Moreover, in the real case, we show
that whenΣ is spiked with a fixed number of subcritical spikes, the type 1 Tracy-Widom
limit TW1 holds for the normalized largest eigenvalue of W N , which extends a
result of Féral and Péché in [J. Math. Phys. 50 (2009) 073302] to the scenario
of nondiagonal Σ and more generally distributed X . In summary, we establish the
Tracy-Widom type universality for the largest eigenvalue of generally distributed
sample covariance matrices under quite light assumptions on &Sigma . Applications
of these limiting results to statistical signal detection and structure recognition
of separable covariance matrices are also discussed.
acknowledgement: "B.Z. was supported in part by NSFC Grant 11071213, ZJNSF
\ Grant R6090034 and SRFDP Grant 20100101110001. P.G. was supported in part
by the Ministry of Education, Singapore, under Grant ARC 14/11. Z.W. was supported
\ in part by the Ministry of Education, Singapore, under Grant ARC 14/11,
\ and by a Grant R-155-000-131-112 at the National University of Singapore\r\n"
article_processing_charge: No
arxiv: 1
author:
- first_name: Zhigang
full_name: Bao, Zhigang
id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
last_name: Bao
orcid: 0000-0003-3036-1475
- first_name: Guangming
full_name: Pan, Guangming
last_name: Pan
- first_name: Wang
full_name: Zhou, Wang
last_name: Zhou
citation:
ama: Bao Z, Pan G, Zhou W. Universality for the largest eigenvalue of sample covariance
matrices with general population. Annals of Statistics. 2015;43(1):382-421.
doi:10.1214/14-AOS1281
apa: Bao, Z., Pan, G., & Zhou, W. (2015). Universality for the largest eigenvalue
of sample covariance matrices with general population. Annals of Statistics.
Institute of Mathematical Statistics. https://doi.org/10.1214/14-AOS1281
chicago: Bao, Zhigang, Guangming Pan, and Wang Zhou. “Universality for the Largest
Eigenvalue of Sample Covariance Matrices with General Population.” Annals of
Statistics. Institute of Mathematical Statistics, 2015. https://doi.org/10.1214/14-AOS1281.
ieee: Z. Bao, G. Pan, and W. Zhou, “Universality for the largest eigenvalue of sample
covariance matrices with general population,” Annals of Statistics, vol.
43, no. 1. Institute of Mathematical Statistics, pp. 382–421, 2015.
ista: Bao Z, Pan G, Zhou W. 2015. Universality for the largest eigenvalue of sample
covariance matrices with general population. Annals of Statistics. 43(1), 382–421.
mla: Bao, Zhigang, et al. “Universality for the Largest Eigenvalue of Sample Covariance
Matrices with General Population.” Annals of Statistics, vol. 43, no. 1,
Institute of Mathematical Statistics, 2015, pp. 382–421, doi:10.1214/14-AOS1281.
short: Z. Bao, G. Pan, W. Zhou, Annals of Statistics 43 (2015) 382–421.
date_created: 2018-12-11T11:52:25Z
date_published: 2015-02-01T00:00:00Z
date_updated: 2025-09-29T11:02:34Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/14-AOS1281
external_id:
arxiv:
- '1304.5690'
isi:
- '000349738500014'
intvolume: ' 43'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1304.5690
month: '02'
oa: 1
oa_version: Preprint
page: 382 - 421
publication: Annals of Statistics
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '5672'
quality_controlled: '1'
status: public
title: Universality for the largest eigenvalue of sample covariance matrices with
general population
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 43
year: '2015'
...
---
_id: '1506'
abstract:
- lang: eng
text: Consider the square random matrix An = (aij)n,n, where {aij:= a(n)ij , i,
j = 1, . . . , n} is a collection of independent real random variables with means
zero and variances one. Under the additional moment condition supn max1≤i,j ≤n
Ea4ij <∞, we prove Girko's logarithmic law of det An in the sense that as n→∞
log | detAn| ? (1/2) log(n-1)! d/→√(1/2) log n N(0, 1).
article_processing_charge: No
arxiv: 1
author:
- first_name: Zhigang
full_name: Bao, Zhigang
id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
last_name: Bao
orcid: 0000-0003-3036-1475
- first_name: Guangming
full_name: Pan, Guangming
last_name: Pan
- first_name: Wang
full_name: Zhou, Wang
last_name: Zhou
citation:
ama: Bao Z, Pan G, Zhou W. The logarithmic law of random determinant. Bernoulli.
2015;21(3):1600-1628. doi:10.3150/14-BEJ615
apa: Bao, Z., Pan, G., & Zhou, W. (2015). The logarithmic law of random determinant.
Bernoulli. Bernoulli Society for Mathematical Statistics and Probability.
https://doi.org/10.3150/14-BEJ615
chicago: Bao, Zhigang, Guangming Pan, and Wang Zhou. “The Logarithmic Law of Random
Determinant.” Bernoulli. Bernoulli Society for Mathematical Statistics
and Probability, 2015. https://doi.org/10.3150/14-BEJ615.
ieee: Z. Bao, G. Pan, and W. Zhou, “The logarithmic law of random determinant,”
Bernoulli, vol. 21, no. 3. Bernoulli Society for Mathematical Statistics
and Probability, pp. 1600–1628, 2015.
ista: Bao Z, Pan G, Zhou W. 2015. The logarithmic law of random determinant. Bernoulli.
21(3), 1600–1628.
mla: Bao, Zhigang, et al. “The Logarithmic Law of Random Determinant.” Bernoulli,
vol. 21, no. 3, Bernoulli Society for Mathematical Statistics and Probability,
2015, pp. 1600–28, doi:10.3150/14-BEJ615.
short: Z. Bao, G. Pan, W. Zhou, Bernoulli 21 (2015) 1600–1628.
date_created: 2018-12-11T11:52:25Z
date_published: 2015-08-01T00:00:00Z
date_updated: 2025-09-23T13:59:56Z
day: '01'
department:
- _id: LaEr
doi: 10.3150/14-BEJ615
external_id:
arxiv:
- '1208.5823'
isi:
- '000356993100012'
intvolume: ' 21'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1208.5823
month: '08'
oa: 1
oa_version: Preprint
page: 1600 - 1628
publication: Bernoulli
publication_status: published
publisher: Bernoulli Society for Mathematical Statistics and Probability
publist_id: '5671'
quality_controlled: '1'
status: public
title: The logarithmic law of random determinant
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 21
year: '2015'
...
---
_id: '1508'
abstract:
- lang: eng
text: We consider generalized Wigner ensembles and general β-ensembles with analytic
potentials for any β ≥ 1. The recent universality results in particular assert
that the local averages of consecutive eigenvalue gaps in the bulk of the spectrum
are universal in the sense that they coincide with those of the corresponding
Gaussian β-ensembles. In this article, we show that local averaging is not necessary
for this result, i.e. we prove that the single gap distributions in the bulk are
universal. In fact, with an additional step, our result can be extended to any
C4(ℝ) potential.
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: Horng
full_name: Yau, Horng
last_name: Yau
citation:
ama: Erdös L, Yau H. Gap universality of generalized Wigner and β ensembles. Journal
of the European Mathematical Society. 2015;17(8):1927-2036. doi:10.4171/JEMS/548
apa: Erdös, L., & Yau, H. (2015). Gap universality of generalized Wigner and
β ensembles. Journal of the European Mathematical Society. European Mathematical
Society. https://doi.org/10.4171/JEMS/548
chicago: Erdös, László, and Horng Yau. “Gap Universality of Generalized Wigner and
β Ensembles.” Journal of the European Mathematical Society. European Mathematical
Society, 2015. https://doi.org/10.4171/JEMS/548.
ieee: L. Erdös and H. Yau, “Gap universality of generalized Wigner and β ensembles,”
Journal of the European Mathematical Society, vol. 17, no. 8. European
Mathematical Society, pp. 1927–2036, 2015.
ista: Erdös L, Yau H. 2015. Gap universality of generalized Wigner and β ensembles.
Journal of the European Mathematical Society. 17(8), 1927–2036.
mla: Erdös, László, and Horng Yau. “Gap Universality of Generalized Wigner and β
Ensembles.” Journal of the European Mathematical Society, vol. 17, no.
8, European Mathematical Society, 2015, pp. 1927–2036, doi:10.4171/JEMS/548.
short: L. Erdös, H. Yau, Journal of the European Mathematical Society 17 (2015)
1927–2036.
date_created: 2018-12-11T11:52:26Z
date_published: 2015-08-01T00:00:00Z
date_updated: 2025-09-23T09:08:38Z
day: '01'
department:
- _id: LaEr
doi: 10.4171/JEMS/548
external_id:
arxiv:
- '1211.3786'
isi:
- '000360822900003'
intvolume: ' 17'
isi: 1
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1211.3786
month: '08'
oa: 1
oa_version: Preprint
page: 1927 - 2036
publication: Journal of the European Mathematical Society
publication_status: published
publisher: European Mathematical Society
publist_id: '5669'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Gap universality of generalized Wigner and β ensembles
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 17
year: '2015'
...
---
_id: '1585'
abstract:
- lang: eng
text: In this paper, we consider the fluctuation of mutual information statistics
of a multiple input multiple output channel communication systems without assuming
that the entries of the channel matrix have zero pseudovariance. To this end,
we also establish a central limit theorem of the linear spectral statistics for
sample covariance matrices under general moment conditions by removing the restrictions
imposed on the second moment and fourth moment on the matrix entries in Bai and
Silverstein (2004).
acknowledgement: "G. Pan was supported by MOE Tier 2 under Grant 2014-T2-2-060 and
in part by Tier 1 under Grant RG25/14 through the Nanyang Technological University,
Singapore. W. Zhou was supported by the National University of Singapore, Singapore,
under Grant R-155-000-131-112.\r\n"
article_processing_charge: No
author:
- first_name: Zhigang
full_name: Bao, Zhigang
id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
last_name: Bao
orcid: 0000-0003-3036-1475
- first_name: Guangming
full_name: Pan, Guangming
last_name: Pan
- first_name: Wang
full_name: Zhou, Wang
last_name: Zhou
citation:
ama: Bao Z, Pan G, Zhou W. Asymptotic mutual information statistics of MIMO channels
and CLT of sample covariance matrices. IEEE Transactions on Information Theory.
2015;61(6):3413-3426. doi:10.1109/TIT.2015.2421894
apa: Bao, Z., Pan, G., & Zhou, W. (2015). Asymptotic mutual information statistics
of MIMO channels and CLT of sample covariance matrices. IEEE Transactions on
Information Theory. IEEE. https://doi.org/10.1109/TIT.2015.2421894
chicago: Bao, Zhigang, Guangming Pan, and Wang Zhou. “Asymptotic Mutual Information
Statistics of MIMO Channels and CLT of Sample Covariance Matrices.” IEEE Transactions
on Information Theory. IEEE, 2015. https://doi.org/10.1109/TIT.2015.2421894.
ieee: Z. Bao, G. Pan, and W. Zhou, “Asymptotic mutual information statistics of
MIMO channels and CLT of sample covariance matrices,” IEEE Transactions on
Information Theory, vol. 61, no. 6. IEEE, pp. 3413–3426, 2015.
ista: Bao Z, Pan G, Zhou W. 2015. Asymptotic mutual information statistics of MIMO
channels and CLT of sample covariance matrices. IEEE Transactions on Information
Theory. 61(6), 3413–3426.
mla: Bao, Zhigang, et al. “Asymptotic Mutual Information Statistics of MIMO Channels
and CLT of Sample Covariance Matrices.” IEEE Transactions on Information Theory,
vol. 61, no. 6, IEEE, 2015, pp. 3413–26, doi:10.1109/TIT.2015.2421894.
short: Z. Bao, G. Pan, W. Zhou, IEEE Transactions on Information Theory 61 (2015)
3413–3426.
date_created: 2018-12-11T11:52:52Z
date_published: 2015-06-01T00:00:00Z
date_updated: 2025-09-23T07:57:31Z
day: '01'
department:
- _id: LaEr
doi: 10.1109/TIT.2015.2421894
external_id:
isi:
- '000354943600029'
intvolume: ' 61'
isi: 1
issue: '6'
language:
- iso: eng
month: '06'
oa_version: None
page: 3413 - 3426
publication: IEEE Transactions on Information Theory
publication_status: published
publisher: IEEE
publist_id: '5586'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Asymptotic mutual information statistics of MIMO channels and CLT of sample
covariance matrices
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 61
year: '2015'
...
---
_id: '1674'
abstract:
- lang: eng
text: We consider N × N random matrices of the form H = W + V where W is a real
symmetric Wigner matrix and V a random or deterministic, real, diagonal matrix
whose entries are independent of W. We assume subexponential decay for the matrix
entries of W and we choose V so that the eigenvalues of W and V are typically
of the same order. For a large class of diagonal matrices V, we show that the
rescaled distribution of the extremal eigenvalues is given by the Tracy-Widom
distribution F1 in the limit of large N. Our proofs also apply to the complex
Hermitian setting, i.e. when W is a complex Hermitian Wigner matrix.
article_number: '1550018'
article_processing_charge: No
arxiv: 1
author:
- first_name: Jioon
full_name: Lee, Jioon
last_name: Lee
- first_name: Kevin
full_name: Schnelli, Kevin
id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
last_name: Schnelli
orcid: 0000-0003-0954-3231
citation:
ama: Lee J, Schnelli K. Edge universality for deformed Wigner matrices. Reviews
in Mathematical Physics. 2015;27(8). doi:10.1142/S0129055X1550018X
apa: Lee, J., & Schnelli, K. (2015). Edge universality for deformed Wigner matrices.
Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/S0129055X1550018X
chicago: Lee, Jioon, and Kevin Schnelli. “Edge Universality for Deformed Wigner
Matrices.” Reviews in Mathematical Physics. World Scientific Publishing,
2015. https://doi.org/10.1142/S0129055X1550018X.
ieee: J. Lee and K. Schnelli, “Edge universality for deformed Wigner matrices,”
Reviews in Mathematical Physics, vol. 27, no. 8. World Scientific Publishing,
2015.
ista: Lee J, Schnelli K. 2015. Edge universality for deformed Wigner matrices. Reviews
in Mathematical Physics. 27(8), 1550018.
mla: Lee, Jioon, and Kevin Schnelli. “Edge Universality for Deformed Wigner Matrices.”
Reviews in Mathematical Physics, vol. 27, no. 8, 1550018, World Scientific
Publishing, 2015, doi:10.1142/S0129055X1550018X.
short: J. Lee, K. Schnelli, Reviews in Mathematical Physics 27 (2015).
date_created: 2018-12-11T11:53:24Z
date_published: 2015-09-01T00:00:00Z
date_updated: 2025-09-23T08:32:19Z
day: '01'
department:
- _id: LaEr
doi: 10.1142/S0129055X1550018X
external_id:
arxiv:
- '1407.8015'
isi:
- '000362566600001'
intvolume: ' 27'
isi: 1
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1407.8015
month: '09'
oa: 1
oa_version: Preprint
publication: Reviews in Mathematical Physics
publication_status: published
publisher: World Scientific Publishing
publist_id: '5475'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Edge universality for deformed Wigner matrices
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 27
year: '2015'
...
---
_id: '1677'
abstract:
- lang: eng
text: We consider real symmetric and complex Hermitian random matrices with the
additional symmetry hxy = hN-y,N-x. The matrix elements are independent (up to
the fourfold symmetry) and not necessarily identically distributed. This ensemble
naturally arises as the Fourier transform of a Gaussian orthogonal ensemble. Italso
occurs as the flip matrix model - an approximation of the two-dimensional Anderson
model at small disorder. We show that the density of states converges to the Wigner
semicircle law despite the new symmetry type. We also prove the local version
of the semicircle law on the optimal scale.
article_number: '103301'
article_processing_charge: No
arxiv: 1
author:
- first_name: Johannes
full_name: Alt, Johannes
id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
last_name: Alt
citation:
ama: Alt J. The local semicircle law for random matrices with a fourfold symmetry.
Journal of Mathematical Physics. 2015;56(10). doi:10.1063/1.4932606
apa: Alt, J. (2015). The local semicircle law for random matrices with a fourfold
symmetry. Journal of Mathematical Physics. American Institute of Physics.
https://doi.org/10.1063/1.4932606
chicago: Alt, Johannes. “The Local Semicircle Law for Random Matrices with a Fourfold
Symmetry.” Journal of Mathematical Physics. American Institute of Physics,
2015. https://doi.org/10.1063/1.4932606.
ieee: J. Alt, “The local semicircle law for random matrices with a fourfold symmetry,”
Journal of Mathematical Physics, vol. 56, no. 10. American Institute of
Physics, 2015.
ista: Alt J. 2015. The local semicircle law for random matrices with a fourfold
symmetry. Journal of Mathematical Physics. 56(10), 103301.
mla: Alt, Johannes. “The Local Semicircle Law for Random Matrices with a Fourfold
Symmetry.” Journal of Mathematical Physics, vol. 56, no. 10, 103301, American
Institute of Physics, 2015, doi:10.1063/1.4932606.
short: J. Alt, Journal of Mathematical Physics 56 (2015).
corr_author: '1'
date_created: 2018-12-11T11:53:25Z
date_published: 2015-10-09T00:00:00Z
date_updated: 2026-04-08T14:11:36Z
day: '09'
department:
- _id: LaEr
doi: 10.1063/1.4932606
ec_funded: 1
external_id:
arxiv:
- '1506.04683'
isi:
- '000364237000026'
intvolume: ' 56'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1506.04683
month: '10'
oa: 1
oa_version: Preprint
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Journal of Mathematical Physics
publication_status: published
publisher: American Institute of Physics
publist_id: '5472'
quality_controlled: '1'
related_material:
record:
- id: '149'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: The local semicircle law for random matrices with a fourfold symmetry
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 56
year: '2015'
...