---
_id: '1012'
abstract:
- lang: eng
text: We prove a new central limit theorem (CLT) for the difference of linear eigenvalue
statistics of a Wigner random matrix H and its minor H and find that the fluctuation
is much smaller than the fluctuations of the individual linear statistics, as
a consequence of the strong correlation between the eigenvalues of H and H. In
particular, our theorem identifies the fluctuation of Kerov's rectangular Young
diagrams, defined by the interlacing eigenvalues ofH and H, around their asymptotic
shape, the Vershik'Kerov'Logan'Shepp curve. Young diagrams equipped with the Plancherel
measure follow the same limiting shape. For this, algebraically motivated, ensemble
a CLT has been obtained in Ivanov and Olshanski [20] which is structurally similar
to our result but the variance is different, indicating that the analogy between
the two models has its limitations. Moreover, our theorem shows that Borodin's
result [7] on the convergence of the spectral distribution of Wigner matrices
to a Gaussian free field also holds in derivative sense.
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: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: Erdös L, Schröder DJ. Fluctuations of rectangular young diagrams of interlacing
wigner eigenvalues. International Mathematics Research Notices. 2018;2018(10):3255-3298.
doi:10.1093/imrn/rnw330
apa: Erdös, L., & Schröder, D. J. (2018). Fluctuations of rectangular young
diagrams of interlacing wigner eigenvalues. International Mathematics Research
Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnw330
chicago: Erdös, László, and Dominik J Schröder. “Fluctuations of Rectangular Young
Diagrams of Interlacing Wigner Eigenvalues.” International Mathematics Research
Notices. Oxford University Press, 2018. https://doi.org/10.1093/imrn/rnw330.
ieee: L. Erdös and D. J. Schröder, “Fluctuations of rectangular young diagrams of
interlacing wigner eigenvalues,” International Mathematics Research Notices,
vol. 2018, no. 10. Oxford University Press, pp. 3255–3298, 2018.
ista: Erdös L, Schröder DJ. 2018. Fluctuations of rectangular young diagrams of
interlacing wigner eigenvalues. International Mathematics Research Notices. 2018(10),
3255–3298.
mla: Erdös, László, and Dominik J. Schröder. “Fluctuations of Rectangular Young
Diagrams of Interlacing Wigner Eigenvalues.” International Mathematics Research
Notices, vol. 2018, no. 10, Oxford University Press, 2018, pp. 3255–98, doi:10.1093/imrn/rnw330.
short: L. Erdös, D.J. Schröder, International Mathematics Research Notices 2018
(2018) 3255–3298.
date_created: 2018-12-11T11:49:41Z
date_published: 2018-05-18T00:00:00Z
date_updated: 2023-09-22T09:44:21Z
day: '18'
department:
- _id: LaEr
doi: 10.1093/imrn/rnw330
ec_funded: 1
external_id:
arxiv:
- '1608.05163'
isi:
- '000441668300009'
intvolume: ' 2018'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1608.05163
month: '05'
oa: 1
oa_version: Preprint
page: 3255-3298
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: International Mathematics Research Notices
publication_identifier:
issn:
- '10737928'
publication_status: published
publisher: Oxford University Press
publist_id: '6383'
quality_controlled: '1'
related_material:
record:
- id: '6179'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 2018
year: '2018'
...
---
_id: '1144'
abstract:
- lang: eng
text: We show that matrix elements of functions of N × N Wigner matrices fluctuate
on a scale of order N−1/2 and we identify the limiting fluctuation. Our result
holds for any function f of the matrix that has bounded variation thus considerably
relaxing the regularity requirement imposed in [7, 11].
acknowledgement: Partially supported by the IST Austria Excellence Scholarship.
article_number: '86'
author:
- 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: Erdös L, Schröder DJ. Fluctuations of functions of Wigner matrices. Electronic
Communications in Probability. 2017;21. doi:10.1214/16-ECP38
apa: Erdös, L., & Schröder, D. J. (2017). Fluctuations of functions of Wigner
matrices. Electronic Communications in Probability. Institute of Mathematical
Statistics. https://doi.org/10.1214/16-ECP38
chicago: Erdös, László, and Dominik J Schröder. “Fluctuations of Functions of Wigner
Matrices.” Electronic Communications in Probability. Institute of Mathematical
Statistics, 2017. https://doi.org/10.1214/16-ECP38.
ieee: L. Erdös and D. J. Schröder, “Fluctuations of functions of Wigner matrices,”
Electronic Communications in Probability, vol. 21. Institute of Mathematical
Statistics, 2017.
ista: Erdös L, Schröder DJ. 2017. Fluctuations of functions of Wigner matrices.
Electronic Communications in Probability. 21, 86.
mla: Erdös, László, and Dominik J. Schröder. “Fluctuations of Functions of Wigner
Matrices.” Electronic Communications in Probability, vol. 21, 86, Institute
of Mathematical Statistics, 2017, doi:10.1214/16-ECP38.
short: L. Erdös, D.J. Schröder, Electronic Communications in Probability 21 (2017).
date_created: 2018-12-11T11:50:23Z
date_published: 2017-01-02T00:00:00Z
date_updated: 2023-09-07T12:54:12Z
day: '02'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1214/16-ECP38
ec_funded: 1
file:
- access_level: open_access
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:18:10Z
date_updated: 2018-12-12T10:18:10Z
file_id: '5329'
file_name: IST-2017-747-v1+1_euclid.ecp.1483347665.pdf
file_size: 440770
relation: main_file
file_date_updated: 2018-12-12T10:18:10Z
has_accepted_license: '1'
intvolume: ' 21'
language:
- iso: eng
month: '01'
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 Communications in Probability
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '6214'
pubrep_id: '747'
quality_controlled: '1'
related_material:
record:
- id: '6179'
relation: dissertation_contains
status: public
scopus_import: 1
status: public
title: Fluctuations of functions of Wigner matrices
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 21
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.'
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-Blackwell. 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-Blackwell, 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-Blackwell, 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-Blackwell, 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.
date_created: 2018-12-11T11:48:08Z
date_published: 2017-09-01T00:00:00Z
date_updated: 2021-01-12T08:12:24Z
day: '01'
department:
- _id: LaEr
doi: 10.1002/cpa.21639
ec_funded: 1
intvolume: ' 70'
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:
- '00103640'
publication_status: published
publisher: Wiley-Blackwell
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: 4435EBFC-F248-11E8-B48F-1D18A9856A87
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
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.
date_created: 2018-12-11T11:48:13Z
date_published: 2017-10-15T00:00:00Z
date_updated: 2023-09-28T11:30:42Z
day: '15'
department:
- _id: LaEr
doi: 10.1016/j.aim.2017.08.028
ec_funded: 1
external_id:
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 319
year: '2017'
...
---
_id: '483'
abstract:
- lang: eng
text: We prove the universality for the eigenvalue gap statistics in the bulk of
the spectrum for band matrices, in the regime where the band width is comparable
with the dimension of the matrix, W ~ N. All previous results concerning universality
of non-Gaussian random matrices are for mean-field models. By relying on a new
mean-field reduction technique, we deduce universality from quantum unique ergodicity
for band matrices.
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: Horng
full_name: Yau, Horng
last_name: Yau
- first_name: Jun
full_name: Yin, Jun
last_name: Yin
citation:
ama: Bourgade P, Erdös L, Yau H, Yin J. Universality for a class of random band
matrices. Advances in Theoretical and Mathematical Physics. 2017;21(3):739-800.
doi:10.4310/ATMP.2017.v21.n3.a5
apa: Bourgade, P., Erdös, L., Yau, H., & Yin, J. (2017). Universality for a
class of random band matrices. Advances in Theoretical and Mathematical Physics.
International Press. https://doi.org/10.4310/ATMP.2017.v21.n3.a5
chicago: Bourgade, Paul, László Erdös, Horng Yau, and Jun Yin. “Universality for
a Class of Random Band Matrices.” Advances in Theoretical and Mathematical
Physics. International Press, 2017. https://doi.org/10.4310/ATMP.2017.v21.n3.a5.
ieee: P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Universality for a class of random
band matrices,” Advances in Theoretical and Mathematical Physics, vol.
21, no. 3. International Press, pp. 739–800, 2017.
ista: Bourgade P, Erdös L, Yau H, Yin J. 2017. Universality for a class of random
band matrices. Advances in Theoretical and Mathematical Physics. 21(3), 739–800.
mla: Bourgade, Paul, et al. “Universality for a Class of Random Band Matrices.”
Advances in Theoretical and Mathematical Physics, vol. 21, no. 3, International
Press, 2017, pp. 739–800, doi:10.4310/ATMP.2017.v21.n3.a5.
short: P. Bourgade, L. Erdös, H. Yau, J. Yin, Advances in Theoretical and Mathematical
Physics 21 (2017) 739–800.
date_created: 2018-12-11T11:46:43Z
date_published: 2017-08-25T00:00:00Z
date_updated: 2021-01-12T08:00:57Z
day: '25'
department:
- _id: LaEr
doi: 10.4310/ATMP.2017.v21.n3.a5
ec_funded: 1
intvolume: ' 21'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1602.02312
month: '08'
oa: 1
oa_version: Submitted Version
page: 739 - 800
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Advances in Theoretical and Mathematical Physics
publication_identifier:
issn:
- '10950761'
publication_status: published
publisher: International Press
publist_id: '7337'
quality_controlled: '1'
scopus_import: 1
status: public
title: Universality for a class of random band matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 21
year: '2017'
...
---
_id: '550'
abstract:
- lang: eng
text: For large random matrices X with independent, centered entries but not necessarily
identical variances, the eigenvalue density of XX* is well-approximated by a deterministic
measure on ℝ. We show that the density of this measure has only square and cubic-root
singularities away from zero. We also extend the bulk local law in [5] to the
vicinity of these singularities.
article_number: '63'
author:
- first_name: Johannes
full_name: Alt, Johannes
id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87
last_name: Alt
citation:
ama: Alt J. Singularities of the density of states of random Gram matrices. Electronic
Communications in Probability. 2017;22. doi:10.1214/17-ECP97
apa: Alt, J. (2017). Singularities of the density of states of random Gram matrices.
Electronic Communications in Probability. Institute of Mathematical Statistics.
https://doi.org/10.1214/17-ECP97
chicago: Alt, Johannes. “Singularities of the Density of States of Random Gram Matrices.”
Electronic Communications in Probability. Institute of Mathematical Statistics,
2017. https://doi.org/10.1214/17-ECP97.
ieee: J. Alt, “Singularities of the density of states of random Gram matrices,”
Electronic Communications in Probability, vol. 22. Institute of Mathematical
Statistics, 2017.
ista: Alt J. 2017. Singularities of the density of states of random Gram matrices.
Electronic Communications in Probability. 22, 63.
mla: Alt, Johannes. “Singularities of the Density of States of Random Gram Matrices.”
Electronic Communications in Probability, vol. 22, 63, Institute of Mathematical
Statistics, 2017, doi:10.1214/17-ECP97.
short: J. Alt, Electronic Communications in Probability 22 (2017).
date_created: 2018-12-11T11:47:07Z
date_published: 2017-11-21T00:00:00Z
date_updated: 2023-09-07T12:38:08Z
day: '21'
ddc:
- '539'
department:
- _id: LaEr
doi: 10.1214/17-ECP97
ec_funded: 1
file:
- access_level: open_access
checksum: 0ec05303a0de190de145654237984c79
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:08:04Z
date_updated: 2020-07-14T12:47:00Z
file_id: '4663'
file_name: IST-2018-926-v1+1_euclid.ecp.1511233247.pdf
file_size: 470876
relation: main_file
file_date_updated: 2020-07-14T12:47:00Z
has_accepted_license: '1'
intvolume: ' 22'
language:
- iso: eng
month: '11'
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 Communications in Probability
publication_identifier:
issn:
- 1083589X
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '7265'
pubrep_id: '926'
quality_controlled: '1'
related_material:
record:
- id: '149'
relation: dissertation_contains
status: public
scopus_import: 1
status: public
title: Singularities of the density of states of 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: '567'
abstract:
- lang: eng
text: "This book is a concise and self-contained introduction of recent techniques
to prove local spectral universality for large random matrices. Random matrix
theory is a fast expanding research area, and this book mainly focuses on the
methods that the authors participated in developing over the past few years. Many
other interesting topics are not included, and neither are several new developments
within the framework of these methods. The authors have chosen instead to present
key concepts that they believe are the core of these methods and should be relevant
for future applications. They keep technicalities to a minimum to make the book
accessible to graduate students. With this in mind, they include in this book
the basic notions and tools for high-dimensional analysis, such as large deviation,
entropy, Dirichlet form, and the logarithmic Sobolev inequality.\r\n"
alternative_title:
- Courant Lecture Notes
article_processing_charge: No
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. A Dynamical Approach to Random Matrix Theory. Vol 28.
American Mathematical Society; 2017. doi:10.1090/cln/028
apa: Erdös, L., & Yau, H. (2017). A Dynamical Approach to Random Matrix Theory
(Vol. 28). American Mathematical Society. https://doi.org/10.1090/cln/028
chicago: Erdös, László, and Horng Yau. A Dynamical Approach to Random Matrix
Theory. Vol. 28. Courant Lecture Notes. American Mathematical Society, 2017.
https://doi.org/10.1090/cln/028.
ieee: L. Erdös and H. Yau, A Dynamical Approach to Random Matrix Theory,
vol. 28. American Mathematical Society, 2017.
ista: Erdös L, Yau H. 2017. A Dynamical Approach to Random Matrix Theory, American
Mathematical Society, 226p.
mla: Erdös, László, and Horng Yau. A Dynamical Approach to Random Matrix Theory.
Vol. 28, American Mathematical Society, 2017, doi:10.1090/cln/028.
short: L. Erdös, H. Yau, A Dynamical Approach to Random Matrix Theory, American
Mathematical Society, 2017.
date_created: 2018-12-11T11:47:13Z
date_published: 2017-01-01T00:00:00Z
date_updated: 2022-05-24T06:57:28Z
day: '01'
department:
- _id: LaEr
doi: 10.1090/cln/028
ec_funded: 1
intvolume: ' 28'
language:
- iso: eng
month: '01'
oa_version: None
page: '226'
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication_identifier:
eisbn:
- 978-1-4704-4194-4
isbn:
- 9-781-4704-3648-3
publication_status: published
publisher: American Mathematical Society
publist_id: '7247'
quality_controlled: '1'
series_title: Courant Lecture Notes
status: public
title: A Dynamical Approach to Random Matrix Theory
type: book
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2017'
...
---
_id: '615'
abstract:
- lang: eng
text: We show that the Dyson Brownian Motion exhibits local universality after a
very short time assuming that local rigidity and level repulsion of the eigenvalues
hold. These conditions are verified, hence bulk spectral universality is proven,
for a large class of Wigner-like matrices, including deformed Wigner ensembles
and ensembles with non-stochastic variance matrices whose limiting densities differ
from Wigner's semicircle law.
author:
- 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: Erdös L, Schnelli K. Universality for random matrix flows with time dependent
density. Annales de l’institut Henri Poincare (B) Probability and Statistics.
2017;53(4):1606-1656. doi:10.1214/16-AIHP765
apa: Erdös, L., & Schnelli, K. (2017). Universality for random matrix flows
with time dependent density. Annales de l’institut Henri Poincare (B) Probability
and Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/16-AIHP765
chicago: Erdös, László, and Kevin Schnelli. “Universality for Random Matrix Flows
with Time Dependent Density.” Annales de l’institut Henri Poincare (B) Probability
and Statistics. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/16-AIHP765.
ieee: L. Erdös and K. Schnelli, “Universality for random matrix flows with time
dependent density,” Annales de l’institut Henri Poincare (B) Probability and
Statistics, vol. 53, no. 4. Institute of Mathematical Statistics, pp. 1606–1656,
2017.
ista: Erdös L, Schnelli K. 2017. Universality for random matrix flows with time
dependent density. Annales de l’institut Henri Poincare (B) Probability and Statistics.
53(4), 1606–1656.
mla: Erdös, László, and Kevin Schnelli. “Universality for Random Matrix Flows with
Time Dependent Density.” Annales de l’institut Henri Poincare (B) Probability
and Statistics, vol. 53, no. 4, Institute of Mathematical Statistics, 2017,
pp. 1606–56, doi:10.1214/16-AIHP765.
short: L. Erdös, K. Schnelli, Annales de l’institut Henri Poincare (B) Probability
and Statistics 53 (2017) 1606–1656.
date_created: 2018-12-11T11:47:30Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2021-01-12T08:06:22Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/16-AIHP765
ec_funded: 1
intvolume: ' 53'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1504.00650
month: '11'
oa: 1
oa_version: Submitted Version
page: 1606 - 1656
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Annales de l'institut Henri Poincare (B) Probability and Statistics
publication_identifier:
issn:
- '02460203'
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '7189'
quality_controlled: '1'
scopus_import: 1
status: public
title: Universality for random matrix flows with time dependent density
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 53
year: '2017'
...
---
_id: '1528'
abstract:
- lang: eng
text: 'We consider N×N Hermitian random matrices H consisting of blocks of size
M≥N6/7. The matrix elements are i.i.d. within the blocks, close to a Gaussian
in the four moment matching sense, but their distribution varies from block to
block to form a block-band structure, with an essential band width M. We show
that the entries of the Green’s function G(z)=(H−z)−1 satisfy the local semicircle
law with spectral parameter z=E+iη down to the real axis for any η≫N−1, using
a combination of the supersymmetry method inspired by Shcherbina (J Stat Phys
155(3): 466–499, 2014) and the Green’s function comparison strategy. Previous
estimates were valid only for η≫M−1. The new estimate also implies that the eigenvectors
in the middle of the spectrum are fully delocalized.'
acknowledgement: "Z. Bao was supported by ERC Advanced Grant RANMAT No. 338804; L.
Erdős was partially supported by ERC Advanced Grant RANMAT No. 338804.\r\nOpen access
funding provided by Institute of Science and Technology (IST Austria). The authors
are very grateful to the anonymous referees for careful reading and valuable comments,
which helped to improve the organization."
article_processing_charge: Yes (via OA deal)
article_type: original
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
citation:
ama: Bao Z, Erdös L. Delocalization for a class of random block band matrices. Probability
Theory and Related Fields. 2017;167(3-4):673-776. doi:10.1007/s00440-015-0692-y
apa: Bao, Z., & Erdös, L. (2017). Delocalization for a class of random block
band matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-015-0692-y
chicago: Bao, Zhigang, and László Erdös. “Delocalization for a Class of Random Block
Band Matrices.” Probability Theory and Related Fields. Springer, 2017.
https://doi.org/10.1007/s00440-015-0692-y.
ieee: Z. Bao and L. Erdös, “Delocalization for a class of random block band matrices,”
Probability Theory and Related Fields, vol. 167, no. 3–4. Springer, pp.
673–776, 2017.
ista: Bao Z, Erdös L. 2017. Delocalization for a class of random block band matrices.
Probability Theory and Related Fields. 167(3–4), 673–776.
mla: Bao, Zhigang, and László Erdös. “Delocalization for a Class of Random Block
Band Matrices.” Probability Theory and Related Fields, vol. 167, no. 3–4,
Springer, 2017, pp. 673–776, doi:10.1007/s00440-015-0692-y.
short: Z. Bao, L. Erdös, Probability Theory and Related Fields 167 (2017) 673–776.
date_created: 2018-12-11T11:52:32Z
date_published: 2017-04-01T00:00:00Z
date_updated: 2023-09-20T09:42:12Z
day: '01'
ddc:
- '530'
department:
- _id: LaEr
doi: 10.1007/s00440-015-0692-y
ec_funded: 1
external_id:
isi:
- '000398842700004'
file:
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checksum: 67afa85ff1e220cbc1f9f477a828513c
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:08:05Z
date_updated: 2020-07-14T12:45:00Z
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file_size: 1615755
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file_date_updated: 2020-07-14T12:45:00Z
has_accepted_license: '1'
intvolume: ' 167'
isi: 1
issue: 3-4
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 673 - 776
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_identifier:
issn:
- '01788051'
publication_status: published
publisher: Springer
publist_id: '5644'
pubrep_id: '489'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Delocalization for a class of random block band matrices
tmp:
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legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
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type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 167
year: '2017'
...
---
_id: '1337'
abstract:
- lang: eng
text: We consider the local eigenvalue distribution of large self-adjoint N×N random
matrices H=H∗ with centered independent entries. In contrast to previous works
the matrix of variances sij=\mathbbmE|hij|2 is not assumed to be stochastic. Hence
the density of states is not the Wigner semicircle law. Its possible shapes are
described in the companion paper (Ajanki et al. in Quadratic Vector Equations
on the Complex Upper Half Plane. arXiv:1506.05095). We show that as N grows, the
resolvent, G(z)=(H−z)−1, converges to a diagonal matrix, diag(m(z)), where m(z)=(m1(z),…,mN(z))
solves the vector equation −1/mi(z)=z+∑jsijmj(z) that has been analyzed in Ajanki
et al. (Quadratic Vector Equations on the Complex Upper Half Plane. arXiv:1506.05095).
We prove a local law down to the smallest spectral resolution scale, and bulk
universality for both real symmetric and complex hermitian symmetry classes.
acknowledgement: 'Open access funding provided by Institute of Science and Technology
(IST Austria). '
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. Universality for general Wigner-type matrices.
Probability Theory and Related Fields. 2017;169(3-4):667-727. doi:10.1007/s00440-016-0740-2
apa: Ajanki, O. H., Erdös, L., & Krüger, T. H. (2017). Universality for general
Wigner-type matrices. Probability Theory and Related Fields. Springer.
https://doi.org/10.1007/s00440-016-0740-2
chicago: Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Universality for
General Wigner-Type Matrices.” Probability Theory and Related Fields. Springer,
2017. https://doi.org/10.1007/s00440-016-0740-2.
ieee: O. H. Ajanki, L. Erdös, and T. H. Krüger, “Universality for general Wigner-type
matrices,” Probability Theory and Related Fields, vol. 169, no. 3–4. Springer,
pp. 667–727, 2017.
ista: Ajanki OH, Erdös L, Krüger TH. 2017. Universality for general Wigner-type
matrices. Probability Theory and Related Fields. 169(3–4), 667–727.
mla: Ajanki, Oskari H., et al. “Universality for General Wigner-Type Matrices.”
Probability Theory and Related Fields, vol. 169, no. 3–4, Springer, 2017,
pp. 667–727, doi:10.1007/s00440-016-0740-2.
short: O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields
169 (2017) 667–727.
date_created: 2018-12-11T11:51:27Z
date_published: 2017-12-01T00:00:00Z
date_updated: 2023-09-20T11:14:17Z
day: '01'
ddc:
- '510'
- '530'
department:
- _id: LaEr
doi: 10.1007/s00440-016-0740-2
ec_funded: 1
external_id:
isi:
- '000414358400002'
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- access_level: open_access
checksum: 29f5a72c3f91e408aeb9e78344973803
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creator: system
date_created: 2018-12-12T10:08:25Z
date_updated: 2020-07-14T12:44:44Z
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issue: 3-4
language:
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month: '12'
oa: 1
oa_version: Published Version
page: 667 - 727
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: Probability Theory and Related Fields
publication_identifier:
issn:
- '01788051'
publication_status: published
publisher: Springer
publist_id: '5930'
pubrep_id: '657'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Universality for general Wigner-type 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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 169
year: '2017'
...
---
_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: 2023-09-22T09:45:23Z
day: '08'
ddc:
- '510'
- '539'
department:
- _id: LaEr
doi: 10.1214/17-EJP42
ec_funded: 1
external_id:
arxiv:
- '1606.07353'
isi:
- '000396611900025'
file:
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creator: system
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file_size: 639384
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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:
- '10836489'
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
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: 2023-09-22T09:27:51Z
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
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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:
- '10836489'
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 22
year: '2017'
...
---
_id: '1207'
abstract:
- lang: eng
text: The eigenvalue distribution of the sum of two large Hermitian matrices, when
one of them is conjugated by a Haar distributed unitary matrix, is asymptotically
given by the free convolution of their spectral distributions. We prove that this
convergence also holds locally in the bulk of the spectrum, down to the optimal
scales larger than the eigenvalue spacing. The corresponding eigenvectors are
fully delocalized. Similar results hold for the sum of two real symmetric matrices,
when one is conjugated by Haar orthogonal matrix.
article_processing_charge: Yes (via OA deal)
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 law of addition of random matrices on optimal
scale. Communications in Mathematical Physics. 2017;349(3):947-990. doi:10.1007/s00220-016-2805-6
apa: Bao, Z., Erdös, L., & Schnelli, K. (2017). Local law of addition of random
matrices on optimal scale. Communications in Mathematical Physics. Springer.
https://doi.org/10.1007/s00220-016-2805-6
chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Law of Addition
of Random Matrices on Optimal Scale.” Communications in Mathematical Physics.
Springer, 2017. https://doi.org/10.1007/s00220-016-2805-6.
ieee: Z. Bao, L. Erdös, and K. Schnelli, “Local law of addition of random matrices
on optimal scale,” Communications in Mathematical Physics, vol. 349, no.
3. Springer, pp. 947–990, 2017.
ista: Bao Z, Erdös L, Schnelli K. 2017. Local law of addition of random matrices
on optimal scale. Communications in Mathematical Physics. 349(3), 947–990.
mla: Bao, Zhigang, et al. “Local Law of Addition of Random Matrices on Optimal Scale.”
Communications in Mathematical Physics, vol. 349, no. 3, Springer, 2017,
pp. 947–90, doi:10.1007/s00220-016-2805-6.
short: Z. Bao, L. Erdös, K. Schnelli, Communications in Mathematical Physics 349
(2017) 947–990.
date_created: 2018-12-11T11:50:43Z
date_published: 2017-02-01T00:00:00Z
date_updated: 2023-09-20T11:16:57Z
day: '01'
ddc:
- '530'
department:
- _id: LaEr
doi: 10.1007/s00220-016-2805-6
ec_funded: 1
external_id:
isi:
- '000393696700005'
file:
- access_level: open_access
checksum: ddff79154c3daf27237de5383b1264a9
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:14:47Z
date_updated: 2020-07-14T12:44:39Z
file_id: '5102'
file_name: IST-2016-722-v1+1_s00220-016-2805-6.pdf
file_size: 1033743
relation: main_file
file_date_updated: 2020-07-14T12:44:39Z
has_accepted_license: '1'
intvolume: ' 349'
isi: 1
issue: '3'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 947 - 990
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- '00103616'
publication_status: published
publisher: Springer
publist_id: '6141'
pubrep_id: '722'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local law of addition of random matrices on optimal scale
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 349
year: '2017'
...
---
_id: '447'
abstract:
- lang: eng
text: We consider last passage percolation (LPP) models with exponentially distributed
random variables, which are linked to the totally asymmetric simple exclusion
process (TASEP). The competition interface for LPP was introduced and studied
in Ferrari and Pimentel (2005a) for cases where the corresponding exclusion process
had a rarefaction fan. Here we consider situations with a shock and determine
the law of the fluctuations of the competition interface around its deter- ministic
law of large number position. We also study the multipoint distribution of the
LPP around the shock, extending our one-point result of Ferrari and Nejjar (2015).
article_processing_charge: No
article_type: original
author:
- first_name: Patrik
full_name: Ferrari, Patrik
last_name: Ferrari
- first_name: Peter
full_name: Nejjar, Peter
id: 4BF426E2-F248-11E8-B48F-1D18A9856A87
last_name: Nejjar
citation:
ama: Ferrari P, Nejjar P. Fluctuations of the competition interface in presence
of shocks. Revista Latino-Americana de Probabilidade e Estatística. 2017;9:299-325.
doi:10.30757/ALEA.v14-17
apa: Ferrari, P., & Nejjar, P. (2017). Fluctuations of the competition interface
in presence of shocks. Revista Latino-Americana de Probabilidade e Estatística.
Instituto Nacional de Matematica Pura e Aplicada. https://doi.org/10.30757/ALEA.v14-17
chicago: Ferrari, Patrik, and Peter Nejjar. “Fluctuations of the Competition Interface
in Presence of Shocks.” Revista Latino-Americana de Probabilidade e Estatística.
Instituto Nacional de Matematica Pura e Aplicada, 2017. https://doi.org/10.30757/ALEA.v14-17.
ieee: P. Ferrari and P. Nejjar, “Fluctuations of the competition interface in presence
of shocks,” Revista Latino-Americana de Probabilidade e Estatística, vol.
9. Instituto Nacional de Matematica Pura e Aplicada, pp. 299–325, 2017.
ista: Ferrari P, Nejjar P. 2017. Fluctuations of the competition interface in presence
of shocks. Revista Latino-Americana de Probabilidade e Estatística. 9, 299–325.
mla: Ferrari, Patrik, and Peter Nejjar. “Fluctuations of the Competition Interface
in Presence of Shocks.” Revista Latino-Americana de Probabilidade e Estatística,
vol. 9, Instituto Nacional de Matematica Pura e Aplicada, 2017, pp. 299–325, doi:10.30757/ALEA.v14-17.
short: P. Ferrari, P. Nejjar, Revista Latino-Americana de Probabilidade e Estatística
9 (2017) 299–325.
date_created: 2018-12-11T11:46:31Z
date_published: 2017-03-23T00:00:00Z
date_updated: 2023-10-10T13:10:32Z
day: '23'
department:
- _id: LaEr
- _id: JaMa
doi: 10.30757/ALEA.v14-17
ec_funded: 1
intvolume: ' 9'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://alea.impa.br/articles/v14/14-17.pdf
month: '03'
oa: 1
oa_version: Submitted Version
page: 299 - 325
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Revista Latino-Americana de Probabilidade e Estatística
publication_status: published
publisher: Instituto Nacional de Matematica Pura e Aplicada
publist_id: '7376'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fluctuations of the competition interface in presence of shocks
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 9
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."
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: 2021-01-12T06:48:43Z
day: '15'
department:
- _id: LaEr
doi: 10.1214/16-AAP1193
ec_funded: 1
intvolume: ' 26'
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 26
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."
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.
date_created: 2018-12-11T11:54:31Z
date_published: 2016-02-01T00:00:00Z
date_updated: 2021-01-12T06:53:49Z
day: '01'
department:
- _id: LaEr
doi: 10.1007/s00440-014-0610-8
ec_funded: 1
intvolume: ' 164'
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 164
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.
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.
date_created: 2018-12-11T11:52:00Z
date_published: 2016-08-01T00:00:00Z
date_updated: 2021-01-12T06:50:42Z
day: '01'
department:
- _id: LaEr
doi: 10.1016/j.jfa.2016.04.006
ec_funded: 1
intvolume: ' 271'
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
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.
date_created: 2018-12-11T11:52:19Z
date_published: 2016-04-01T00:00:00Z
date_updated: 2021-01-12T06:51:05Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s10955-016-1479-y
ec_funded: 1
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'
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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. '
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.
date_created: 2018-12-11T11:53:00Z
date_published: 2016-07-01T00:00:00Z
date_updated: 2021-01-12T06:51:58Z
day: '01'
department:
- _id: LaEr
doi: 10.1007/s00023-015-0456-3
ec_funded: 1
intvolume: ' 17'
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 17
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. "
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: 2021-01-12T06:49:10Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/15-AOP1023
ec_funded: 1
intvolume: ' 44'
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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 44
year: '2016'
...