---
_id: '10405'
abstract:
- lang: eng
text: 'We consider large non-Hermitian random matrices X with complex, independent,
identically distributed centred entries and show that the linear statistics of
their eigenvalues are asymptotically Gaussian for test functions having 2+ϵ derivatives.
Previously this result was known only for a few special cases; either the test
functions were required to be analytic [72], or the distribution of the matrix
elements needed to be Gaussian [73], or at least match the Gaussian up to the
first four moments [82, 56]. We find the exact dependence of the limiting variance
on the fourth cumulant that was not known before. The proof relies on two novel
ingredients: (i) a local law for a product of two resolvents of the Hermitisation
of X with different spectral parameters and (ii) a coupling of several weakly
dependent Dyson Brownian motions. These methods are also the key inputs for our
analogous results on the linear eigenvalue statistics of real matrices X that
are presented in the companion paper [32]. '
acknowledgement: L.E. would like to thank Nathanaël Berestycki and D.S.would like
to thank Nina Holden for valuable discussions on the Gaussian freefield.G.C. and
L.E. are partially supported by ERC Advanced Grant No. 338804.G.C. received funding
from the European Union’s Horizon 2020 research and in-novation programme under
the Marie Skłodowska-Curie Grant Agreement No.665385. D.S. is supported by Dr. Max
Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: Cipolloni G, Erdös L, Schröder DJ. Central limit theorem for linear eigenvalue
statistics of non-Hermitian random matrices. Communications on Pure and Applied
Mathematics. 2023;76(5):946-1034. doi:10.1002/cpa.22028
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). Central limit theorem
for linear eigenvalue statistics of non-Hermitian random matrices. Communications
on Pure and Applied Mathematics. Wiley. https://doi.org/10.1002/cpa.22028
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Central Limit
Theorem for Linear Eigenvalue Statistics of Non-Hermitian Random Matrices.” Communications
on Pure and Applied Mathematics. Wiley, 2023. https://doi.org/10.1002/cpa.22028.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Central limit theorem for linear
eigenvalue statistics of non-Hermitian random matrices,” Communications on
Pure and Applied Mathematics, vol. 76, no. 5. Wiley, pp. 946–1034, 2023.
ista: Cipolloni G, Erdös L, Schröder DJ. 2023. Central limit theorem for linear
eigenvalue statistics of non-Hermitian random matrices. Communications on Pure
and Applied Mathematics. 76(5), 946–1034.
mla: Cipolloni, Giorgio, et al. “Central Limit Theorem for Linear Eigenvalue Statistics
of Non-Hermitian Random Matrices.” Communications on Pure and Applied Mathematics,
vol. 76, no. 5, Wiley, 2023, pp. 946–1034, doi:10.1002/cpa.22028.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Communications on Pure and Applied
Mathematics 76 (2023) 946–1034.
corr_author: '1'
date_created: 2021-12-05T23:01:41Z
date_published: 2023-05-01T00:00:00Z
date_updated: 2025-03-31T16:00:54Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1002/cpa.22028
ec_funded: 1
external_id:
arxiv:
- '1912.04100'
isi:
- '000724652500001'
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checksum: 8346bc2642afb4ccb7f38979f41df5d9
content_type: application/pdf
creator: dernst
date_created: 2023-10-04T09:21:48Z
date_updated: 2023-10-04T09:21:48Z
file_id: '14388'
file_name: 2023_CommPureMathematics_Cipolloni.pdf
file_size: 803440
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language:
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oa: 1
oa_version: Published Version
page: 946-1034
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publisher: Wiley
quality_controlled: '1'
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status: public
title: Central limit theorem for linear eigenvalue statistics of non-Hermitian random
matrices
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
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short: CC BY-NC-ND (4.0)
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year: '2023'
...
---
_id: '15013'
abstract:
- lang: eng
text: We consider random n×n matrices X with independent and centered entries and
a general variance profile. We show that the spectral radius of X converges with
very high probability to the square root of the spectral radius of the variance
matrix of X when n tends to infinity. We also establish the optimal rate of convergence,
that is a new result even for general i.i.d. matrices beyond the explicitly solvable
Gaussian cases. The main ingredient is the proof of the local inhomogeneous circular
law [arXiv:1612.07776] at the spectral edge.
acknowledgement: Partially supported by ERC Starting Grant RandMat No. 715539 and
the SwissMap grant of Swiss National Science Foundation. Partially supported by
ERC Advanced Grant RanMat No. 338804. Partially supported by the Hausdorff Center
for Mathematics in Bonn.
article_processing_charge: No
article_type: original
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. Spectral radius of random matrices with independent
entries. Probability and Mathematical Physics. 2021;2(2):221-280. doi:10.2140/pmp.2021.2.221
apa: Alt, J., Erdös, L., & Krüger, T. H. (2021). Spectral radius of random matrices
with independent entries. Probability and Mathematical Physics. Mathematical
Sciences Publishers. https://doi.org/10.2140/pmp.2021.2.221
chicago: Alt, Johannes, László Erdös, and Torben H Krüger. “Spectral Radius of Random
Matrices with Independent Entries.” Probability and Mathematical Physics.
Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/pmp.2021.2.221.
ieee: J. Alt, L. Erdös, and T. H. Krüger, “Spectral radius of random matrices with
independent entries,” Probability and Mathematical Physics, vol. 2, no.
2. Mathematical Sciences Publishers, pp. 221–280, 2021.
ista: Alt J, Erdös L, Krüger TH. 2021. Spectral radius of random matrices with independent
entries. Probability and Mathematical Physics. 2(2), 221–280.
mla: Alt, Johannes, et al. “Spectral Radius of Random Matrices with Independent
Entries.” Probability and Mathematical Physics, vol. 2, no. 2, Mathematical
Sciences Publishers, 2021, pp. 221–80, doi:10.2140/pmp.2021.2.221.
short: J. Alt, L. Erdös, T.H. Krüger, Probability and Mathematical Physics 2 (2021)
221–280.
corr_author: '1'
date_created: 2024-02-18T23:01:03Z
date_published: 2021-05-21T00:00:00Z
date_updated: 2025-04-15T08:05:02Z
day: '21'
department:
- _id: LaEr
doi: 10.2140/pmp.2021.2.221
ec_funded: 1
external_id:
arxiv:
- '1907.13631'
intvolume: ' 2'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1907.13631
month: '05'
oa: 1
oa_version: Preprint
page: 221-280
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Probability and Mathematical Physics
publication_identifier:
eissn:
- 2690-1005
issn:
- 2690-0998
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Spectral radius of random matrices with independent entries
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2
year: '2021'
...
---
_id: '9912'
abstract:
- lang: eng
text: "In the customary random matrix model for transport in quantum dots with M
internal degrees of freedom coupled to a chaotic environment via \U0001D441≪\U0001D440
channels, the density \U0001D70C of transmission eigenvalues is computed from
a specific invariant ensemble for which explicit formula for the joint probability
density of all eigenvalues is available. We revisit this problem in the large
N regime allowing for (i) arbitrary ratio \U0001D719:=\U0001D441/\U0001D440≤1;
and (ii) general distributions for the matrix elements of the Hamiltonian of the
quantum dot. In the limit \U0001D719→0, we recover the formula for the density
\U0001D70C that Beenakker (Rev Mod Phys 69:731–808, 1997) has derived for a special
matrix ensemble. We also prove that the inverse square root singularity of the
density at zero and full transmission in Beenakker’s formula persists for any
\U0001D719<1 but in the borderline case \U0001D719=1 an anomalous \U0001D706−2/3
singularity arises at zero. To access this level of generality, we develop the
theory of global and local laws on the spectral density of a large class of noncommutative
rational expressions in large random matrices with i.i.d. entries."
acknowledgement: The authors are very grateful to Yan Fyodorov for discussions on
the physical background and for providing references, and to the anonymous referee
for numerous valuable remarks.
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: Yuriy
full_name: Nemish, Yuriy
id: 4D902E6A-F248-11E8-B48F-1D18A9856A87
last_name: Nemish
orcid: 0000-0002-7327-856X
citation:
ama: Erdös L, Krüger TH, Nemish Y. Scattering in quantum dots via noncommutative
rational functions. Annales Henri Poincaré . 2021;22:4205–4269. doi:10.1007/s00023-021-01085-6
apa: Erdös, L., Krüger, T. H., & Nemish, Y. (2021). Scattering in quantum dots
via noncommutative rational functions. Annales Henri Poincaré . Springer
Nature. https://doi.org/10.1007/s00023-021-01085-6
chicago: Erdös, László, Torben H Krüger, and Yuriy Nemish. “Scattering in Quantum
Dots via Noncommutative Rational Functions.” Annales Henri Poincaré . Springer
Nature, 2021. https://doi.org/10.1007/s00023-021-01085-6.
ieee: L. Erdös, T. H. Krüger, and Y. Nemish, “Scattering in quantum dots via noncommutative
rational functions,” Annales Henri Poincaré , vol. 22. Springer Nature,
pp. 4205–4269, 2021.
ista: Erdös L, Krüger TH, Nemish Y. 2021. Scattering in quantum dots via noncommutative
rational functions. Annales Henri Poincaré . 22, 4205–4269.
mla: Erdös, László, et al. “Scattering in Quantum Dots via Noncommutative Rational
Functions.” Annales Henri Poincaré , vol. 22, Springer Nature, 2021, pp.
4205–4269, doi:10.1007/s00023-021-01085-6.
short: L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré 22 (2021) 4205–4269.
date_created: 2021-08-15T22:01:29Z
date_published: 2021-12-01T00:00:00Z
date_updated: 2025-04-15T08:04:59Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00023-021-01085-6
ec_funded: 1
external_id:
arxiv:
- '1911.05112'
isi:
- '000681531500001'
file:
- access_level: open_access
checksum: 8d6bac0e2b0a28539608b0538a8e3b38
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date_created: 2022-05-12T12:50:27Z
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file_name: 2021_AnnHenriPoincare_Erdoes.pdf
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month: '12'
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name: Random matrices, universality and disordered quantum systems
publication: 'Annales Henri Poincaré '
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eissn:
- 1424-0661
issn:
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publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Scattering in quantum dots via noncommutative rational functions
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 22
year: '2021'
...
---
_id: '8601'
abstract:
- lang: eng
text: We consider large non-Hermitian real or complex random matrices X with independent,
identically distributed centred entries. We prove that their local eigenvalue
statistics near the spectral edge, the unit circle, coincide with those of the
Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result
is the non-Hermitian counterpart of the universality of the Tracy–Widom distribution
at the spectral edges of the Wigner ensemble.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: Cipolloni G, Erdös L, Schröder DJ. Edge universality for non-Hermitian random
matrices. Probability Theory and Related Fields. 2021. doi:10.1007/s00440-020-01003-7
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Edge universality for
non-Hermitian random matrices. Probability Theory and Related Fields. Springer
Nature. https://doi.org/10.1007/s00440-020-01003-7
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Edge Universality
for Non-Hermitian Random Matrices.” Probability Theory and Related Fields.
Springer Nature, 2021. https://doi.org/10.1007/s00440-020-01003-7.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Edge universality for non-Hermitian
random matrices,” Probability Theory and Related Fields. Springer Nature,
2021.
ista: Cipolloni G, Erdös L, Schröder DJ. 2021. Edge universality for non-Hermitian
random matrices. Probability Theory and Related Fields.
mla: Cipolloni, Giorgio, et al. “Edge Universality for Non-Hermitian Random Matrices.”
Probability Theory and Related Fields, Springer Nature, 2021, doi:10.1007/s00440-020-01003-7.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields
(2021).
corr_author: '1'
date_created: 2020-10-04T22:01:37Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2026-04-02T14:03:52Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00440-020-01003-7
ec_funded: 1
external_id:
arxiv:
- '1908.00969'
isi:
- '000572724600002'
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checksum: 611ae28d6055e1e298d53a57beb05ef4
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creator: dernst
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date_updated: 2020-10-05T14:53:40Z
file_id: '8612'
file_name: 2020_ProbTheory_Cipolloni.pdf
file_size: 497032
relation: main_file
success: 1
file_date_updated: 2020-10-05T14:53:40Z
has_accepted_license: '1'
isi: 1
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
project:
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name: IST Austria Open Access Fund
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- 1432-2064
issn:
- 0178-8051
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Edge universality for non-Hermitian random matrices
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2021'
...
---
_id: '9550'
abstract:
- lang: eng
text: 'We prove that the energy of any eigenvector of a sum of several independent
large Wigner matrices is equally distributed among these matrices with very high
precision. This shows a particularly strong microcanonical form of the equipartition
principle for quantum systems whose components are modelled by Wigner matrices. '
acknowledgement: The first author is supported in part by Hong Kong RGC Grant GRF
16301519 and NSFC 11871425. The second author is supported in part by ERC Advanced
Grant RANMAT 338804. The third author is supported in part by Swedish Research Council
Grant VR-2017-05195 and the Knut and Alice Wallenberg Foundation
article_number: e44
article_processing_charge: No
article_type: original
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. Equipartition principle for Wigner matrices. Forum
of Mathematics, Sigma. 2021;9. doi:10.1017/fms.2021.38
apa: Bao, Z., Erdös, L., & Schnelli, K. (2021). Equipartition principle for
Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press.
https://doi.org/10.1017/fms.2021.38
chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Equipartition Principle
for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge University
Press, 2021. https://doi.org/10.1017/fms.2021.38.
ieee: Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,”
Forum of Mathematics, Sigma, vol. 9. Cambridge University Press, 2021.
ista: Bao Z, Erdös L, Schnelli K. 2021. Equipartition principle for Wigner matrices.
Forum of Mathematics, Sigma. 9, e44.
mla: Bao, Zhigang, et al. “Equipartition Principle for Wigner Matrices.” Forum
of Mathematics, Sigma, vol. 9, e44, Cambridge University Press, 2021, doi:10.1017/fms.2021.38.
short: Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021).
date_created: 2021-06-13T22:01:33Z
date_published: 2021-05-27T00:00:00Z
date_updated: 2026-04-07T08:36:39Z
day: '27'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1017/fms.2021.38
ec_funded: 1
external_id:
arxiv:
- '2008.07061'
isi:
- '000654960800001'
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intvolume: ' 9'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
project:
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call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Forum of Mathematics, Sigma
publication_identifier:
eissn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Equipartition principle for Wigner matrices
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user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 9
year: '2021'
...
---
OA_place: publisher
_id: '9022'
abstract:
- lang: eng
text: "In the first part of the thesis we consider Hermitian random matrices. Firstly,
we consider sample covariance matrices XX∗ with X having independent identically
distributed (i.i.d.) centred entries. We prove a Central Limit Theorem for differences
of linear statistics of XX∗ and its minor after removing the first column of X.
Secondly, we consider Wigner-type matrices and prove that the eigenvalue statistics
near cusp singularities of the limiting density of states are universal and that
they form a Pearcey process. Since the limiting eigenvalue distribution admits
only square root (edge) and cubic root (cusp) singularities, this concludes the
third and last remaining case of the Wigner-Dyson-Mehta universality conjecture.
The main technical ingredients are an optimal local law at the cusp, and the proof
of the fast relaxation to equilibrium of the Dyson Brownian motion in the cusp
regime.\r\nIn the second part we consider non-Hermitian matrices X with centred
i.i.d. entries. We normalise the entries of X to have variance N −1. It is well
known that the empirical eigenvalue density converges to the uniform distribution
on the unit disk (circular law). In the first project, we prove universality of
the local eigenvalue statistics close to the edge of the spectrum. This is the
non-Hermitian analogue of the TracyWidom universality at the Hermitian edge. Technically
we analyse the evolution of the spectral distribution of X along the Ornstein-Uhlenbeck
flow for very long time\r\n(up to t = +∞). In the second project, we consider
linear statistics of eigenvalues for macroscopic test functions f in the Sobolev
space H2+ϵ and prove their convergence to the projection of the Gaussian Free
Field on the unit disk. We prove this result for non-Hermitian matrices with real
or complex entries. The main technical ingredients are: (i) local law for products
of two resolvents at different spectral parameters, (ii) analysis of correlated
Dyson Brownian motions.\r\nIn the third and final part we discuss the mathematically
rigorous application of supersymmetric techniques (SUSY ) to give a lower tail
estimate of the lowest singular value of X − z, with z ∈ C. More precisely, we
use superbosonisation formula to give an integral representation of the resolvent
of (X − z)(X − z)∗ which reduces to two and three contour integrals in the complex
and real case, respectively. The rigorous analysis of these integrals is quite
challenging since simple saddle point analysis cannot be applied (the main contribution
comes from a non-trivial manifold). Our result\r\nimproves classical smoothing
inequalities in the regime |z| ≈ 1; this result is essential to prove edge universality
for i.i.d. non-Hermitian matrices."
acknowledgement: I gratefully acknowledge the financial support from the European
Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
Grant Agreement No. 665385 and my advisor’s ERC Advanced Grant No. 338804.
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
citation:
ama: Cipolloni G. Fluctuations in the spectrum of random matrices. 2021. doi:10.15479/AT:ISTA:9022
apa: Cipolloni, G. (2021). Fluctuations in the spectrum of random matrices.
Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:9022
chicago: Cipolloni, Giorgio. “Fluctuations in the Spectrum of Random Matrices.”
Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/AT:ISTA:9022.
ieee: G. Cipolloni, “Fluctuations in the spectrum of random matrices,” Institute
of Science and Technology Austria, 2021.
ista: Cipolloni G. 2021. Fluctuations in the spectrum of random matrices. Institute
of Science and Technology Austria.
mla: Cipolloni, Giorgio. Fluctuations in the Spectrum of Random Matrices.
Institute of Science and Technology Austria, 2021, doi:10.15479/AT:ISTA:9022.
short: G. Cipolloni, Fluctuations in the Spectrum of Random Matrices, Institute
of Science and Technology Austria, 2021.
corr_author: '1'
date_created: 2021-01-21T18:16:54Z
date_published: 2021-01-25T00:00:00Z
date_updated: 2026-04-08T06:59:33Z
day: '25'
ddc:
- '510'
degree_awarded: PhD
department:
- _id: GradSch
- _id: LaEr
doi: 10.15479/AT:ISTA:9022
ec_funded: 1
file:
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has_accepted_license: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: '380'
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
status: public
supervisor:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
title: Fluctuations in the spectrum of random matrices
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2021'
...
---
_id: '15063'
abstract:
- lang: eng
text: We consider the least singular value of a large random matrix with real or
complex i.i.d. Gaussian entries shifted by a constant z∈C. We prove an optimal
lower tail estimate on this singular value in the critical regime where z is around
the spectral edge, thus improving the classical bound of Sankar, Spielman and
Teng (SIAM J. Matrix Anal. Appl. 28:2 (2006), 446–476) for the particular shift-perturbation
in the edge regime. Lacking Brézin–Hikami formulas in the real case, we rely on
the superbosonization formula (Comm. Math. Phys. 283:2 (2008), 343–395).
acknowledgement: Partially supported by ERC Advanced Grant No. 338804. This project
has received funding from the European Union’s Horizon 2020 research and innovation
programme under the Marie Sklodowska-Curie Grant Agreement No. 66538
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: Cipolloni G, Erdös L, Schröder DJ. Optimal lower bound on the least singular
value of the shifted Ginibre ensemble. Probability and Mathematical Physics.
2020;1(1):101-146. doi:10.2140/pmp.2020.1.101
apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2020). Optimal lower bound
on the least singular value of the shifted Ginibre ensemble. Probability and
Mathematical Physics. Mathematical Sciences Publishers. https://doi.org/10.2140/pmp.2020.1.101
chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Lower
Bound on the Least Singular Value of the Shifted Ginibre Ensemble.” Probability
and Mathematical Physics. Mathematical Sciences Publishers, 2020. https://doi.org/10.2140/pmp.2020.1.101.
ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal lower bound on the least
singular value of the shifted Ginibre ensemble,” Probability and Mathematical
Physics, vol. 1, no. 1. Mathematical Sciences Publishers, pp. 101–146, 2020.
ista: Cipolloni G, Erdös L, Schröder DJ. 2020. Optimal lower bound on the least
singular value of the shifted Ginibre ensemble. Probability and Mathematical Physics.
1(1), 101–146.
mla: Cipolloni, Giorgio, et al. “Optimal Lower Bound on the Least Singular Value
of the Shifted Ginibre Ensemble.” Probability and Mathematical Physics,
vol. 1, no. 1, Mathematical Sciences Publishers, 2020, pp. 101–46, doi:10.2140/pmp.2020.1.101.
short: G. Cipolloni, L. Erdös, D.J. Schröder, Probability and Mathematical Physics
1 (2020) 101–146.
corr_author: '1'
date_created: 2024-03-04T10:27:57Z
date_published: 2020-11-16T00:00:00Z
date_updated: 2025-07-10T11:51:06Z
day: '16'
department:
- _id: LaEr
doi: 10.2140/pmp.2020.1.101
ec_funded: 1
external_id:
arxiv:
- '1908.01653'
intvolume: ' 1'
issue: '1'
keyword:
- General Medicine
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1908.01653
month: '11'
oa: 1
oa_version: Preprint
page: 101-146
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: Probability and Mathematical Physics
publication_identifier:
issn:
- 2690-0998
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal lower bound on the least singular value of the shifted Ginibre ensemble
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 1
year: '2020'
...
---
_id: '10862'
abstract:
- lang: eng
text: We consider the sum of two large Hermitian matrices A and B with a Haar unitary
conjugation bringing them into a general relative position. We prove that the
eigenvalue density on the scale slightly above the local eigenvalue spacing is
asymptotically given by the free additive convolution of the laws of A and B as
the dimension of the matrix increases. This implies optimal rigidity of the eigenvalues
and optimal rate of convergence in Voiculescu's theorem. Our previous works [4],
[5] established these results in the bulk spectrum, the current paper completely
settles the problem at the spectral edges provided they have the typical square-root
behavior. The key element of our proof is to compensate the deterioration of the
stability of the subordination equations by sharp error estimates that properly
account for the local density near the edge. Our results also hold if the Haar
unitary matrix is replaced by the Haar orthogonal matrix.
acknowledgement: Partially supported by ERC Advanced Grant RANMAT No. 338804.
article_number: '108639'
article_processing_charge: No
article_type: original
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
last_name: Schnelli
citation:
ama: Bao Z, Erdös L, Schnelli K. Spectral rigidity for addition of random matrices
at the regular edge. Journal of Functional Analysis. 2020;279(7). doi:10.1016/j.jfa.2020.108639
apa: Bao, Z., Erdös, L., & Schnelli, K. (2020). Spectral rigidity for addition
of random matrices at the regular edge. Journal of Functional Analysis.
Elsevier. https://doi.org/10.1016/j.jfa.2020.108639
chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Spectral Rigidity for
Addition of Random Matrices at the Regular Edge.” Journal of Functional Analysis.
Elsevier, 2020. https://doi.org/10.1016/j.jfa.2020.108639.
ieee: Z. Bao, L. Erdös, and K. Schnelli, “Spectral rigidity for addition of random
matrices at the regular edge,” Journal of Functional Analysis, vol. 279,
no. 7. Elsevier, 2020.
ista: Bao Z, Erdös L, Schnelli K. 2020. Spectral rigidity for addition of random
matrices at the regular edge. Journal of Functional Analysis. 279(7), 108639.
mla: Bao, Zhigang, et al. “Spectral Rigidity for Addition of Random Matrices at
the Regular Edge.” Journal of Functional Analysis, vol. 279, no. 7, 108639,
Elsevier, 2020, doi:10.1016/j.jfa.2020.108639.
short: Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 279 (2020).
corr_author: '1'
date_created: 2022-03-18T10:18:59Z
date_published: 2020-10-15T00:00:00Z
date_updated: 2025-04-15T08:05:01Z
day: '15'
department:
- _id: LaEr
doi: 10.1016/j.jfa.2020.108639
ec_funded: 1
external_id:
arxiv:
- '1708.01597'
isi:
- '000559623200009'
intvolume: ' 279'
isi: 1
issue: '7'
keyword:
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1708.01597
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 Functional Analysis
publication_identifier:
issn:
- 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Spectral rigidity for addition of random matrices at the regular edge
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 279
year: '2020'
...
---
_id: '9104'
abstract:
- lang: eng
text: We consider the free additive convolution of two probability measures μ and
ν on the real line and show that μ ⊞ v is supported on a single interval if μ
and ν each has single interval support. Moreover, the density of μ ⊞ ν is proven
to vanish as a square root near the edges of its support if both μ and ν have
power law behavior with exponents between −1 and 1 near their edges. In particular,
these results show the ubiquity of the conditions in our recent work on optimal
local law at the spectral edges for addition of random matrices [5].
acknowledgement: "Supported in part by Hong Kong RGC Grant ECS 26301517.\r\nSupported
in part by ERC Advanced Grant RANMAT No. 338804.\r\nSupported in part by the Knut
and Alice Wallenberg Foundation and the Swedish Research Council Grant VR-2017-05195."
article_processing_charge: No
article_type: original
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. On the support of the free additive convolution.
Journal d’Analyse Mathematique. 2020;142:323-348. doi:10.1007/s11854-020-0135-2
apa: Bao, Z., Erdös, L., & Schnelli, K. (2020). On the support of the free additive
convolution. Journal d’Analyse Mathematique. Springer Nature. https://doi.org/10.1007/s11854-020-0135-2
chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “On the Support of the
Free Additive Convolution.” Journal d’Analyse Mathematique. Springer Nature,
2020. https://doi.org/10.1007/s11854-020-0135-2.
ieee: Z. Bao, L. Erdös, and K. Schnelli, “On the support of the free additive convolution,”
Journal d’Analyse Mathematique, vol. 142. Springer Nature, pp. 323–348,
2020.
ista: Bao Z, Erdös L, Schnelli K. 2020. On the support of the free additive convolution.
Journal d’Analyse Mathematique. 142, 323–348.
mla: Bao, Zhigang, et al. “On the Support of the Free Additive Convolution.” Journal
d’Analyse Mathematique, vol. 142, Springer Nature, 2020, pp. 323–48, doi:10.1007/s11854-020-0135-2.
short: Z. Bao, L. Erdös, K. Schnelli, Journal d’Analyse Mathematique 142 (2020)
323–348.
date_created: 2021-02-07T23:01:15Z
date_published: 2020-11-01T00:00:00Z
date_updated: 2025-07-10T12:01:37Z
day: '01'
department:
- _id: LaEr
doi: 10.1007/s11854-020-0135-2
ec_funded: 1
external_id:
arxiv:
- '1804.11199'
isi:
- '000611879400008'
intvolume: ' 142'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1804.11199
month: '11'
oa: 1
oa_version: Preprint
page: 323-348
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Journal d'Analyse Mathematique
publication_identifier:
eissn:
- 1565-8538
issn:
- 0021-7670
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the support of the free additive convolution
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 142
year: '2020'
...
---
_id: '6488'
abstract:
- lang: eng
text: We prove a central limit theorem for the difference of linear eigenvalue statistics
of a sample covariance matrix W˜ and its minor W. We find that the fluctuation
of this difference is much smaller than those of the individual linear statistics,
as a consequence of the strong correlation between the eigenvalues of W˜ and W.
Our result identifies the fluctuation of the spatial derivative of the approximate
Gaussian field in the recent paper by Dumitru and Paquette. Unlike in a similar
result for Wigner matrices, for sample covariance matrices, the fluctuation may
entirely vanish.
article_number: '2050006'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
citation:
ama: 'Cipolloni G, Erdös L. Fluctuations for differences of linear eigenvalue statistics
for sample covariance matrices. Random Matrices: Theory and Application.
2020;9(3). doi:10.1142/S2010326320500069'
apa: 'Cipolloni, G., & Erdös, L. (2020). Fluctuations for differences of linear
eigenvalue statistics for sample covariance matrices. Random Matrices: Theory
and Application. World Scientific Publishing. https://doi.org/10.1142/S2010326320500069'
chicago: 'Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of
Linear Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices:
Theory and Application. World Scientific Publishing, 2020. https://doi.org/10.1142/S2010326320500069.'
ieee: 'G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue
statistics for sample covariance matrices,” Random Matrices: Theory and Application,
vol. 9, no. 3. World Scientific Publishing, 2020.'
ista: 'Cipolloni G, Erdös L. 2020. Fluctuations for differences of linear eigenvalue
statistics for sample covariance matrices. Random Matrices: Theory and Application.
9(3), 2050006.'
mla: 'Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear
Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices: Theory
and Application, vol. 9, no. 3, 2050006, World Scientific Publishing, 2020,
doi:10.1142/S2010326320500069.'
short: 'G. Cipolloni, L. Erdös, Random Matrices: Theory and Application 9 (2020).'
date_created: 2019-05-26T21:59:14Z
date_published: 2020-07-01T00:00:00Z
date_updated: 2025-07-10T11:53:26Z
day: '01'
department:
- _id: LaEr
doi: 10.1142/S2010326320500069
ec_funded: 1
external_id:
arxiv:
- '1806.08751'
isi:
- '000547464400001'
intvolume: ' 9'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1806.08751
month: '07'
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
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: 'Random Matrices: Theory and Application'
publication_identifier:
eissn:
- 2010-3271
issn:
- 2010-3263
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fluctuations for differences of linear eigenvalue statistics for sample covariance
matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 9
year: '2020'
...
---
_id: '7512'
abstract:
- lang: eng
text: We consider general self-adjoint polynomials in several independent random
matrices whose entries are centered and have the same variance. We show that under
certain conditions the local law holds up to the optimal scale, i.e., the eigenvalue
density on scales just above the eigenvalue spacing follows the global density
of states which is determined by free probability theory. We prove that these
conditions hold for general homogeneous polynomials of degree two and for symmetrized
products of independent matrices with i.i.d. entries, thus establishing the optimal
bulk local law for these classes of ensembles. In particular, we generalize a
similar result of Anderson for anticommutator. For more general polynomials our
conditions are effectively checkable numerically.
acknowledgement: "The authors are grateful to Oskari Ajanki for his invaluable help
at the initial stage of this project, to Serban Belinschi for useful discussions,
to Alexander Tikhomirov for calling our attention to the model example in Section
6.2 and to the anonymous referee for suggesting to simplify certain proofs. Erdös:
Partially funded by ERC Advanced Grant RANMAT No. 338804\r\n"
article_number: '108507'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: Yuriy
full_name: Nemish, Yuriy
id: 4D902E6A-F248-11E8-B48F-1D18A9856A87
last_name: Nemish
orcid: 0000-0002-7327-856X
citation:
ama: Erdös L, Krüger TH, Nemish Y. Local laws for polynomials of Wigner matrices.
Journal of Functional Analysis. 2020;278(12). doi:10.1016/j.jfa.2020.108507
apa: Erdös, L., Krüger, T. H., & Nemish, Y. (2020). Local laws for polynomials
of Wigner matrices. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2020.108507
chicago: Erdös, László, Torben H Krüger, and Yuriy Nemish. “Local Laws for Polynomials
of Wigner Matrices.” Journal of Functional Analysis. Elsevier, 2020. https://doi.org/10.1016/j.jfa.2020.108507.
ieee: L. Erdös, T. H. Krüger, and Y. Nemish, “Local laws for polynomials of Wigner
matrices,” Journal of Functional Analysis, vol. 278, no. 12. Elsevier,
2020.
ista: Erdös L, Krüger TH, Nemish Y. 2020. Local laws for polynomials of Wigner matrices.
Journal of Functional Analysis. 278(12), 108507.
mla: Erdös, László, et al. “Local Laws for Polynomials of Wigner Matrices.” Journal
of Functional Analysis, vol. 278, no. 12, 108507, Elsevier, 2020, doi:10.1016/j.jfa.2020.108507.
short: L. Erdös, T.H. Krüger, Y. Nemish, Journal of Functional Analysis 278 (2020).
date_created: 2020-02-23T23:00:36Z
date_published: 2020-07-01T00:00:00Z
date_updated: 2025-07-10T11:54:43Z
day: '01'
department:
- _id: LaEr
doi: 10.1016/j.jfa.2020.108507
ec_funded: 1
external_id:
arxiv:
- '1804.11340'
isi:
- '000522798900001'
intvolume: ' 278'
isi: 1
issue: '12'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1804.11340
month: '07'
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 Functional Analysis
publication_identifier:
eissn:
- 1096-0783
issn:
- 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local laws for polynomials of Wigner matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 278
year: '2020'
...
---
_id: '6185'
abstract:
- lang: eng
text: For complex Wigner-type matrices, i.e. Hermitian random matrices with independent,
not necessarily identically distributed entries above the diagonal, we show that
at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue
statistics are universal and form a Pearcey process. Since the density of states
typically exhibits only square root or cubic root cusp singularities, our work
complements previous results on the bulk and edge universality and it thus completes
the resolution of the Wigner–Dyson–Mehta universality conjecture for the last
remaining universality type in the complex Hermitian class. Our analysis holds
not only for exact cusps, but approximate cusps as well, where an extended Pearcey
process emerges. As a main technical ingredient we prove an optimal local law
at the cusp for both symmetry classes. This result is also the key input in the
companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where
the cusp universality for real symmetric Wigner-type matrices is proven. The novel
cusp fluctuation mechanism is also essential for the recent results on the spectral
radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random
matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian
edge universality (Cipolloni et al. in Edge universality for non-Hermitian random
matrices, 2019. arXiv:1908.00969).
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria). The authors are very grateful to Johannes Alt for numerous discussions
on the Dyson equation and for his invaluable help in adjusting [10] to the needs
of the present work.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- 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, Krüger TH, Schröder DJ. Cusp universality for random matrices I:
Local law and the complex Hermitian case. Communications in Mathematical Physics.
2020;378:1203-1278. doi:10.1007/s00220-019-03657-4'
apa: 'Erdös, L., Krüger, T. H., & Schröder, D. J. (2020). Cusp universality
for random matrices I: Local law and the complex Hermitian case. Communications
in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03657-4'
chicago: 'Erdös, László, Torben H Krüger, and Dominik J Schröder. “Cusp Universality
for Random Matrices I: Local Law and the Complex Hermitian Case.” Communications
in Mathematical Physics. Springer Nature, 2020. https://doi.org/10.1007/s00220-019-03657-4.'
ieee: 'L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random
matrices I: Local law and the complex Hermitian case,” Communications in Mathematical
Physics, vol. 378. Springer Nature, pp. 1203–1278, 2020.'
ista: 'Erdös L, Krüger TH, Schröder DJ. 2020. Cusp universality for random matrices
I: Local law and the complex Hermitian case. Communications in Mathematical Physics.
378, 1203–1278.'
mla: 'Erdös, László, et al. “Cusp Universality for Random Matrices I: Local Law
and the Complex Hermitian Case.” Communications in Mathematical Physics,
vol. 378, Springer Nature, 2020, pp. 1203–78, doi:10.1007/s00220-019-03657-4.'
short: L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics
378 (2020) 1203–1278.
date_created: 2019-03-28T10:21:15Z
date_published: 2020-09-01T00:00:00Z
date_updated: 2026-04-08T13:55:03Z
day: '01'
ddc:
- '530'
- '510'
department:
- _id: LaEr
doi: 10.1007/s00220-019-03657-4
ec_funded: 1
external_id:
arxiv:
- '1809.03971'
isi:
- '000529483000001'
file:
- access_level: open_access
checksum: c3a683e2afdcea27afa6880b01e53dc2
content_type: application/pdf
creator: dernst
date_created: 2020-11-18T11:14:37Z
date_updated: 2020-11-18T11:14:37Z
file_id: '8771'
file_name: 2020_CommMathPhysics_Erdoes.pdf
file_size: 2904574
relation: main_file
success: 1
file_date_updated: 2020-11-18T11:14:37Z
has_accepted_license: '1'
intvolume: ' 378'
isi: 1
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 1203-1278
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: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
record:
- id: '6179'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: 'Cusp universality for random matrices I: Local law and the complex Hermitian
case'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 378
year: '2020'
...
---
_id: '6184'
abstract:
- lang: eng
text: We prove edge universality for a general class of correlated real symmetric
or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also
applies to internal edges of the self-consistent density of states. In particular,
we establish a strong form of band rigidity which excludes mismatches between
location and label of eigenvalues close to internal edges in these general models.
article_processing_charge: No
article_type: original
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
- 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: 'Alt J, Erdös L, Krüger TH, Schröder DJ. Correlated random matrices: Band rigidity
and edge universality. Annals of Probability. 2020;48(2):963-1001. doi:10.1214/19-AOP1379'
apa: 'Alt, J., Erdös, L., Krüger, T. H., & Schröder, D. J. (2020). Correlated
random matrices: Band rigidity and edge universality. Annals of Probability.
Institute of Mathematical Statistics. https://doi.org/10.1214/19-AOP1379'
chicago: 'Alt, Johannes, László Erdös, Torben H Krüger, and Dominik J Schröder.
“Correlated Random Matrices: Band Rigidity and Edge Universality.” Annals of
Probability. Institute of Mathematical Statistics, 2020. https://doi.org/10.1214/19-AOP1379.'
ieee: 'J. Alt, L. Erdös, T. H. Krüger, and D. J. Schröder, “Correlated random matrices:
Band rigidity and edge universality,” Annals of Probability, vol. 48, no.
2. Institute of Mathematical Statistics, pp. 963–1001, 2020.'
ista: 'Alt J, Erdös L, Krüger TH, Schröder DJ. 2020. Correlated random matrices:
Band rigidity and edge universality. Annals of Probability. 48(2), 963–1001.'
mla: 'Alt, Johannes, et al. “Correlated Random Matrices: Band Rigidity and Edge
Universality.” Annals of Probability, vol. 48, no. 2, Institute of Mathematical
Statistics, 2020, pp. 963–1001, doi:10.1214/19-AOP1379.'
short: J. Alt, L. Erdös, T.H. Krüger, D.J. Schröder, Annals of Probability 48 (2020)
963–1001.
date_created: 2019-03-28T09:20:08Z
date_published: 2020-03-01T00:00:00Z
date_updated: 2026-04-08T14:11:36Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/19-AOP1379
ec_funded: 1
external_id:
arxiv:
- '1804.07744'
isi:
- '000528269100013'
intvolume: ' 48'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1804.07744
month: '03'
oa: 1
oa_version: Preprint
page: 963-1001
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_identifier:
issn:
- 0091-1798
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
related_material:
record:
- id: '6179'
relation: dissertation_contains
status: public
- id: '149'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: 'Correlated random matrices: Band rigidity and edge universality'
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 48
year: '2020'
...
---
_id: '8175'
abstract:
- lang: eng
text: We study edge asymptotics of poissonized Plancherel-type measures on skew
Young diagrams (integer partitions). These measures can be seen as generalizations
of those studied by Baik--Deift--Johansson and Baik--Rains in resolving Ulam's
problem on longest increasing subsequences of random permutations and the last
passage percolation (corner growth) discrete versions thereof. Moreover they interpolate
between said measures and the uniform measure on partitions. In the new KPZ-like
1/3 exponent edge scaling limit with logarithmic corrections, we find new probability
distributions generalizing the classical Tracy--Widom GUE, GOE and GSE distributions
from the theory of random matrices.
acknowledgement: "D.B. is especially grateful to Patrik Ferrari for suggesting simplifications
in Section 3 and\r\nto Alessandra Occelli for suggesting the name for the models
of Section 2.\r\n"
article_number: '34'
article_processing_charge: No
arxiv: 1
author:
- first_name: Dan
full_name: Betea, Dan
last_name: Betea
- first_name: Jérémie
full_name: Bouttier, Jérémie
last_name: Bouttier
- first_name: Peter
full_name: Nejjar, Peter
id: 4BF426E2-F248-11E8-B48F-1D18A9856A87
last_name: Nejjar
- first_name: Mirjana
full_name: Vuletíc, Mirjana
last_name: Vuletíc
citation:
ama: 'Betea D, Bouttier J, Nejjar P, Vuletíc M. New edge asymptotics of skew Young
diagrams via free boundaries. In: Proceedings on the 31st International Conference
on Formal Power Series and Algebraic Combinatorics. Formal Power Series and
Algebraic Combinatorics; 2019.'
apa: 'Betea, D., Bouttier, J., Nejjar, P., & Vuletíc, M. (2019). New edge asymptotics
of skew Young diagrams via free boundaries. In Proceedings on the 31st International
Conference on Formal Power Series and Algebraic Combinatorics. Ljubljana,
Slovenia: Formal Power Series and Algebraic Combinatorics.'
chicago: Betea, Dan, Jérémie Bouttier, Peter Nejjar, and Mirjana Vuletíc. “New Edge
Asymptotics of Skew Young Diagrams via Free Boundaries.” In Proceedings on
the 31st International Conference on Formal Power Series and Algebraic Combinatorics.
Formal Power Series and Algebraic Combinatorics, 2019.
ieee: D. Betea, J. Bouttier, P. Nejjar, and M. Vuletíc, “New edge asymptotics of
skew Young diagrams via free boundaries,” in Proceedings on the 31st International
Conference on Formal Power Series and Algebraic Combinatorics, Ljubljana,
Slovenia, 2019.
ista: 'Betea D, Bouttier J, Nejjar P, Vuletíc M. 2019. New edge asymptotics of skew
Young diagrams via free boundaries. Proceedings on the 31st International Conference
on Formal Power Series and Algebraic Combinatorics. FPSAC: International Conference
on Formal Power Series and Algebraic Combinatorics, 34.'
mla: Betea, Dan, et al. “New Edge Asymptotics of Skew Young Diagrams via Free Boundaries.”
Proceedings on the 31st International Conference on Formal Power Series and
Algebraic Combinatorics, 34, Formal Power Series and Algebraic Combinatorics,
2019.
short: D. Betea, J. Bouttier, P. Nejjar, M. Vuletíc, in:, Proceedings on the 31st
International Conference on Formal Power Series and Algebraic Combinatorics, Formal
Power Series and Algebraic Combinatorics, 2019.
conference:
end_date: 2019-07-05
location: Ljubljana, Slovenia
name: 'FPSAC: International Conference on Formal Power Series and Algebraic Combinatorics'
start_date: 2019-07-01
date_created: 2020-07-26T22:01:04Z
date_published: 2019-07-01T00:00:00Z
date_updated: 2021-01-12T08:17:18Z
day: '01'
department:
- _id: LaEr
ec_funded: 1
external_id:
arxiv:
- '1902.08750'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1902.08750
month: '07'
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
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Proceedings on the 31st International Conference on Formal Power Series
and Algebraic Combinatorics
publication_status: published
publisher: Formal Power Series and Algebraic Combinatorics
quality_controlled: '1'
scopus_import: '1'
status: public
title: New edge asymptotics of skew Young diagrams via free boundaries
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2019'
...
---
_id: '6511'
abstract:
- lang: eng
text: Let U and V be two independent N by N random matrices that are distributed
according to Haar measure on U(N). Let Σ be a nonnegative deterministic N by N
matrix. The single ring theorem [Ann. of Math. (2) 174 (2011) 1189–1217] asserts
that the empirical eigenvalue distribution of the matrix X:=UΣV∗ converges weakly,
in the limit of large N, to a deterministic measure which is supported on a single
ring centered at the origin in ℂ. Within the bulk regime, that is, in the interior
of the single ring, we establish the convergence of the empirical eigenvalue distribution
on the optimal local scale of order N−1/2+ε and establish the optimal convergence
rate. The same results hold true when U and V are Haar distributed on O(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: 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 single ring theorem on optimal scale. Annals
of Probability. 2019;47(3):1270-1334. doi:10.1214/18-AOP1284
apa: Bao, Z., Erdös, L., & Schnelli, K. (2019). Local single ring theorem on
optimal scale. Annals of Probability. Institute of Mathematical Statistics.
https://doi.org/10.1214/18-AOP1284
chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Single Ring Theorem
on Optimal Scale.” Annals of Probability. Institute of Mathematical Statistics,
2019. https://doi.org/10.1214/18-AOP1284.
ieee: Z. Bao, L. Erdös, and K. Schnelli, “Local single ring theorem on optimal scale,”
Annals of Probability, vol. 47, no. 3. Institute of Mathematical Statistics,
pp. 1270–1334, 2019.
ista: Bao Z, Erdös L, Schnelli K. 2019. Local single ring theorem on optimal scale.
Annals of Probability. 47(3), 1270–1334.
mla: Bao, Zhigang, et al. “Local Single Ring Theorem on Optimal Scale.” Annals
of Probability, vol. 47, no. 3, Institute of Mathematical Statistics, 2019,
pp. 1270–334, doi:10.1214/18-AOP1284.
short: Z. Bao, L. Erdös, K. Schnelli, Annals of Probability 47 (2019) 1270–1334.
date_created: 2019-06-02T21:59:13Z
date_published: 2019-05-01T00:00:00Z
date_updated: 2025-07-10T11:53:28Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/18-AOP1284
ec_funded: 1
external_id:
arxiv:
- '1612.05920'
isi:
- '000466616100003'
intvolume: ' 47'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1612.05920
month: '05'
oa: 1
oa_version: Preprint
page: 1270-1334
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_identifier:
issn:
- 0091-1798
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local single ring theorem on optimal scale
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 47
year: '2019'
...
---
_id: '72'
abstract:
- lang: eng
text: We consider the totally asymmetric simple exclusion process (TASEP) with non-random
initial condition having density ρ on ℤ− and λ on ℤ+, and a second class particle
initially at the origin. For ρ<λ, there is a shock and the second class particle
moves with speed 1−λ−ρ. For large time t, we show that the position of the second
class particle fluctuates on a t1/3 scale and determine its limiting law. We also
obtain the limiting distribution of the number of steps made by the second class
particle until time t.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Patrick
full_name: Ferrari, Patrick
last_name: Ferrari
- first_name: Promit
full_name: Ghosal, Promit
last_name: Ghosal
- first_name: Peter
full_name: Nejjar, Peter
id: 4BF426E2-F248-11E8-B48F-1D18A9856A87
last_name: Nejjar
citation:
ama: Ferrari P, Ghosal P, Nejjar P. Limit law of a second class particle in TASEP
with non-random initial condition. Annales de l’institut Henri Poincare (B)
Probability and Statistics. 2019;55(3):1203-1225. doi:10.1214/18-AIHP916
apa: Ferrari, P., Ghosal, P., & Nejjar, P. (2019). Limit law of a second class
particle in TASEP with non-random initial condition. Annales de l’institut
Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics.
https://doi.org/10.1214/18-AIHP916
chicago: Ferrari, Patrick, Promit Ghosal, and Peter Nejjar. “Limit Law of a Second
Class Particle in TASEP with Non-Random Initial Condition.” Annales de l’institut
Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics,
2019. https://doi.org/10.1214/18-AIHP916.
ieee: P. Ferrari, P. Ghosal, and P. Nejjar, “Limit law of a second class particle
in TASEP with non-random initial condition,” Annales de l’institut Henri Poincare
(B) Probability and Statistics, vol. 55, no. 3. Institute of Mathematical
Statistics, pp. 1203–1225, 2019.
ista: Ferrari P, Ghosal P, Nejjar P. 2019. Limit law of a second class particle
in TASEP with non-random initial condition. Annales de l’institut Henri Poincare
(B) Probability and Statistics. 55(3), 1203–1225.
mla: Ferrari, Patrick, et al. “Limit Law of a Second Class Particle in TASEP with
Non-Random Initial Condition.” Annales de l’institut Henri Poincare (B) Probability
and Statistics, vol. 55, no. 3, Institute of Mathematical Statistics, 2019,
pp. 1203–25, doi:10.1214/18-AIHP916.
short: P. Ferrari, P. Ghosal, P. Nejjar, Annales de l’institut Henri Poincare (B)
Probability and Statistics 55 (2019) 1203–1225.
date_created: 2018-12-11T11:44:29Z
date_published: 2019-09-25T00:00:00Z
date_updated: 2025-04-14T07:27:49Z
day: '25'
department:
- _id: LaEr
- _id: JaMa
doi: 10.1214/18-AIHP916
ec_funded: 1
external_id:
arxiv:
- '1710.02323'
isi:
- '000487763200001'
intvolume: ' 55'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1710.02323
month: '09'
oa: 1
oa_version: Preprint
page: 1203-1225
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Annales de l'institut Henri Poincare (B) Probability and Statistics
publication_identifier:
issn:
- 0246-0203
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Limit law of a second class particle in TASEP with non-random initial condition
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 55
year: '2019'
...
---
_id: '429'
abstract:
- lang: eng
text: We consider real symmetric or complex hermitian random matrices with correlated
entries. We prove local laws for the resolvent and universality of the local eigenvalue
statistics in the bulk of the spectrum. The correlations have fast decay but are
otherwise of general form. The key novelty is the detailed stability analysis
of the corresponding matrix valued Dyson equation whose solution is the deterministic
limit of the resolvent.
acknowledgement: "Open access funding provided by Institute of Science and Technology
(IST Austria).\r\n"
article_processing_charge: Yes (via OA deal)
article_type: original
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. Stability of the matrix Dyson equation and random
matrices with correlations. Probability Theory and Related Fields. 2019;173(1-2):293–373.
doi:10.1007/s00440-018-0835-z
apa: Ajanki, O. H., Erdös, L., & Krüger, T. H. (2019). Stability of the matrix
Dyson equation and random matrices with correlations. Probability Theory and
Related Fields. Springer. https://doi.org/10.1007/s00440-018-0835-z
chicago: Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Stability of the
Matrix Dyson Equation and Random Matrices with Correlations.” Probability Theory
and Related Fields. Springer, 2019. https://doi.org/10.1007/s00440-018-0835-z.
ieee: O. H. Ajanki, L. Erdös, and T. H. Krüger, “Stability of the matrix Dyson equation
and random matrices with correlations,” Probability Theory and Related Fields,
vol. 173, no. 1–2. Springer, pp. 293–373, 2019.
ista: Ajanki OH, Erdös L, Krüger TH. 2019. Stability of the matrix Dyson equation
and random matrices with correlations. Probability Theory and Related Fields.
173(1–2), 293–373.
mla: Ajanki, Oskari H., et al. “Stability of the Matrix Dyson Equation and Random
Matrices with Correlations.” Probability Theory and Related Fields, vol.
173, no. 1–2, Springer, 2019, pp. 293–373, doi:10.1007/s00440-018-0835-z.
short: O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields
173 (2019) 293–373.
corr_author: '1'
date_created: 2018-12-11T11:46:25Z
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date_updated: 2026-04-03T09:46:51Z
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doi: 10.1007/s00440-018-0835-z
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title: Stability of the matrix Dyson equation and random matrices with correlations
tmp:
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name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
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abstract:
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text: "In the first part of this thesis we consider large random matrices with arbitrary
expectation and a general slowly decaying correlation among its entries. We prove
universality of the local eigenvalue statistics and optimal local laws for the
resolvent in the bulk and edge regime. The main novel tool is a systematic diagrammatic
control of a multivariate cumulant expansion.\r\nIn the second part we consider
Wigner-type matrices and show that at any cusp singularity of the limiting eigenvalue
distribution the local eigenvalue statistics are uni- versal and form a Pearcey
process. Since the density of states typically exhibits only square root or cubic
root cusp singularities, our work complements previous results on the bulk and
edge universality and it thus completes the resolution of the Wigner- Dyson-Mehta
universality conjecture for the last remaining universality type. Our analysis
holds not only for exact cusps, but approximate cusps as well, where an ex- tended
Pearcey process emerges. As a main technical ingredient we prove an optimal local
law at the cusp, and extend the fast relaxation to equilibrium of the Dyson Brow-
nian motion to the cusp regime.\r\nIn the third and final part we explore the
entrywise linear statistics of Wigner ma- trices and identify the fluctuations
for a large class of test functions with little regularity. This enables us to
study the rectangular Young diagram obtained from the interlacing eigenvalues
of the random matrix and its minor, and we find that, despite having the same
limit, the fluctuations differ from those of the algebraic Young tableaux equipped
with the Plancharel measure."
alternative_title:
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author:
- 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: 'Schröder DJ. From Dyson to Pearcey: Universal statistics in random matrix
theory. 2019. doi:10.15479/AT:ISTA:th6179'
apa: 'Schröder, D. J. (2019). From Dyson to Pearcey: Universal statistics in
random matrix theory. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th6179'
chicago: 'Schröder, Dominik J. “From Dyson to Pearcey: Universal Statistics in Random
Matrix Theory.” Institute of Science and Technology Austria, 2019. https://doi.org/10.15479/AT:ISTA:th6179.'
ieee: 'D. J. Schröder, “From Dyson to Pearcey: Universal statistics in random matrix
theory,” Institute of Science and Technology Austria, 2019.'
ista: 'Schröder DJ. 2019. From Dyson to Pearcey: Universal statistics in random
matrix theory. Institute of Science and Technology Austria.'
mla: 'Schröder, Dominik J. From Dyson to Pearcey: Universal Statistics in Random
Matrix Theory. Institute of Science and Technology Austria, 2019, doi:10.15479/AT:ISTA:th6179.'
short: 'D.J. Schröder, From Dyson to Pearcey: Universal Statistics in Random Matrix
Theory, Institute of Science and Technology Austria, 2019.'
corr_author: '1'
date_created: 2019-03-28T08:58:59Z
date_published: 2019-03-18T00:00:00Z
date_updated: 2026-04-08T13:55:03Z
day: '18'
ddc:
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degree_awarded: PhD
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doi: 10.15479/AT:ISTA:th6179
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call_identifier: FP7
grant_number: '338804'
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issn:
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publisher: Institute of Science and Technology Austria
related_material:
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status: public
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relation: part_of_dissertation
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relation: part_of_dissertation
status: public
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relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
title: 'From Dyson to Pearcey: Universal statistics in random matrix theory'
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2019'
...
---
_id: '6182'
abstract:
- lang: eng
text: "We consider large random matrices with a general slowly decaying correlation
among its entries. We prove universality of the local eigenvalue statistics and
optimal local laws for the resolvent away from the spectral edges, generalizing
the recent result of Ajanki et al. [‘Stability of the matrix Dyson equation and
random matrices with correlations’, Probab. Theory Related Fields 173(1–2) (2019),
293–373] to allow slow correlation decay and arbitrary expectation. The main novel
tool is\r\na systematic diagrammatic control of a multivariate cumulant expansion."
article_number: e8
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- 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, Krüger TH, Schröder DJ. Random matrices with slow correlation decay.
Forum of Mathematics, Sigma. 2019;7. doi:10.1017/fms.2019.2
apa: Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Random matrices with
slow correlation decay. Forum of Mathematics, Sigma. Cambridge University
Press. https://doi.org/10.1017/fms.2019.2
chicago: Erdös, László, Torben H Krüger, and Dominik J Schröder. “Random Matrices
with Slow Correlation Decay.” Forum of Mathematics, Sigma. Cambridge University
Press, 2019. https://doi.org/10.1017/fms.2019.2.
ieee: L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation
decay,” Forum of Mathematics, Sigma, vol. 7. Cambridge University Press,
2019.
ista: Erdös L, Krüger TH, Schröder DJ. 2019. Random matrices with slow correlation
decay. Forum of Mathematics, Sigma. 7, e8.
mla: Erdös, László, et al. “Random Matrices with Slow Correlation Decay.” Forum
of Mathematics, Sigma, vol. 7, e8, Cambridge University Press, 2019, doi:10.1017/fms.2019.2.
short: L. Erdös, T.H. Krüger, D.J. Schröder, Forum of Mathematics, Sigma 7 (2019).
corr_author: '1'
date_created: 2019-03-28T09:05:23Z
date_published: 2019-03-26T00:00:00Z
date_updated: 2026-04-08T13:55:03Z
day: '26'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1017/fms.2019.2
ec_funded: 1
external_id:
arxiv:
- '1705.10661'
isi:
- '000488847100001'
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language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
project:
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call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Forum of Mathematics, Sigma
publication_identifier:
eissn:
- 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
related_material:
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relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Random matrices with slow correlation decay
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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)
short: CC BY (4.0)
type: journal_article
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 7
year: '2019'
...
---
_id: '6186'
abstract:
- lang: eng
text: "We prove that the local eigenvalue statistics of real symmetric Wigner-type\r\nmatrices
near the cusp points of the eigenvalue density are universal. Together\r\nwith
the companion paper [arXiv:1809.03971], which proves the same result for\r\nthe
complex Hermitian symmetry class, this completes the last remaining case of\r\nthe
Wigner-Dyson-Mehta universality conjecture after bulk and edge\r\nuniversalities
have been established in the last years. We extend the recent\r\nDyson Brownian
motion analysis at the edge [arXiv:1712.03881] to the cusp\r\nregime using the
optimal local law from [arXiv:1809.03971] and the accurate\r\nlocal shape analysis
of the density from [arXiv:1506.05095, arXiv:1804.07752].\r\nWe also present a
PDE-based method to improve the estimate on eigenvalue\r\nrigidity via the maximum
principle of the heat flow related to the Dyson\r\nBrownian motion."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Giorgio
full_name: Cipolloni, Giorgio
id: 42198EFA-F248-11E8-B48F-1D18A9856A87
last_name: Cipolloni
orcid: 0000-0002-4901-7992
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Torben H
full_name: Krüger, Torben H
id: 3020C786-F248-11E8-B48F-1D18A9856A87
last_name: Krüger
orcid: 0000-0002-4821-3297
- first_name: Dominik J
full_name: Schröder, Dominik J
id: 408ED176-F248-11E8-B48F-1D18A9856A87
last_name: Schröder
orcid: 0000-0002-2904-1856
citation:
ama: 'Cipolloni G, Erdös L, Krüger TH, Schröder DJ. Cusp universality for random
matrices, II: The real symmetric case. Pure and Applied Analysis . 2019;1(4):615–707.
doi:10.2140/paa.2019.1.615'
apa: 'Cipolloni, G., Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Cusp
universality for random matrices, II: The real symmetric case. Pure and Applied
Analysis . MSP. https://doi.org/10.2140/paa.2019.1.615'
chicago: 'Cipolloni, Giorgio, László Erdös, Torben H Krüger, and Dominik J Schröder.
“Cusp Universality for Random Matrices, II: The Real Symmetric Case.” Pure
and Applied Analysis . MSP, 2019. https://doi.org/10.2140/paa.2019.1.615.'
ieee: 'G. Cipolloni, L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality
for random matrices, II: The real symmetric case,” Pure and Applied Analysis
, vol. 1, no. 4. MSP, pp. 615–707, 2019.'
ista: 'Cipolloni G, Erdös L, Krüger TH, Schröder DJ. 2019. Cusp universality for
random matrices, II: The real symmetric case. Pure and Applied Analysis . 1(4),
615–707.'
mla: 'Cipolloni, Giorgio, et al. “Cusp Universality for Random Matrices, II: The
Real Symmetric Case.” Pure and Applied Analysis , vol. 1, no. 4, MSP, 2019,
pp. 615–707, doi:10.2140/paa.2019.1.615.'
short: G. Cipolloni, L. Erdös, T.H. Krüger, D.J. Schröder, Pure and Applied Analysis 1
(2019) 615–707.
date_created: 2019-03-28T10:21:17Z
date_published: 2019-10-12T00:00:00Z
date_updated: 2026-04-08T13:55:02Z
day: '12'
department:
- _id: LaEr
doi: 10.2140/paa.2019.1.615
ec_funded: 1
external_id:
arxiv:
- '1811.04055'
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issue: '4'
language:
- iso: eng
main_file_link:
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url: https://arxiv.org/abs/1811.04055
month: '10'
oa: 1
oa_version: Preprint
page: 615–707
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: 'Pure and Applied Analysis '
publication_identifier:
eissn:
- 2578-5885
issn:
- 2578-5893
publication_status: published
publisher: MSP
quality_controlled: '1'
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title: 'Cusp universality for random matrices, II: The real symmetric case'
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user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 1
year: '2019'
...