Random matrices beyond Wigner-Dyson-Mehta

Project Information

RMTBEYOND

Grant agreement ID: 101020331

Project website

DOI

10.3030/101020331

EC signature date 18 July 2021

Start date 1 October 2021

End date 30 September 2026

Funded under

EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 912 439,00

EU contribution

€ 1 912 439,00

1 912 439,00

Coordinated by

INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA
Austria

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Dynamics of a rank-one multiplicative perturbation of a unitary matrix

Author(s): Guillaume Dubach; Jana Reker
Published in: Random Matrices: Theory and Applications, Issue 5, 2024, ISSN 2010-3263
Publisher: World Scientific Publishing
DOI: 10.1142/s2010326324500072

Normal typicality and dynamical typicality for a random block-band matrix model

Author(s): László Erdős, Joscha Henheik, Cornelia Vogel
Published in: Letters in Mathematical Physics, Issue 116, 2026, ISSN 1573-0530
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s11005-025-02037-5

Dynamics of a rank-one perturbation of a Hermitian matrix

Author(s): Dubach G, Erdös L
Published in: Electronic Communications in Probability, 2023, ISSN 1083-589X
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/23-ecp516

Spiked multiplicative random matrices and principal components

Author(s): Ding, Xiucai; Ji, Hong Chang
Published in: Stochastic Processes and their Applications, 2023, ISSN 0304-4149
Publisher: Elsevier BV
DOI: 10.1016/j.spa.2023.05.009

Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices

Author(s): Giorgio Cipolloni; László Erdős; Joscha Henheik; Dominik Schröder
Published in: Journal of Functional Analysis, Issue 19, 2024, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2024.110495

Optimal decay of eigenvector overlap for non-Hermitian random matrices

Author(s): Giorgio Cipolloni, László Erdős, Yuanyuan Xu
Published in: Journal of Functional Analysis, Issue 290, 2025, Page(s) 111180, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2025.111180

Small deviation estimates for the largest eigenvalue of Wigner matrices

Author(s): Erdös L, Xu Y
Published in: Bernoulli, 2023, ISSN 1350-7265
Publisher: Chapman & Hall
DOI: 10.3150/22-bej1490

Gaussian fluctuations in the equipartition principle for Wigner matrices

Author(s): Giorgio Cipolloni; László Erdős; Joscha Henheik; Oleksii Kolupaiev
Published in: Forum of Mathematics, Sigma, Vol 11 (2023), 2023, ISSN 2050-5094
Publisher: Cambridge University Press
DOI: 10.1017/fms.2023.70

Wegner estimate and upper bound on the eigenvalue condition number of non‐Hermitian random matrices

Author(s): Erdős, László; Ji, Hong Chang
Published in: Communications on Pure and Applied Mathematics, Issue 3, 2024, ISSN 0010-3640
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/cpa.22201

Fluctuation Moments for Regular Functions of Wigner Matrices

Author(s): Jana Reker
Published in: Mathematical Physics, Analysis and Geometry, Issue 12, 2024, ISSN 1385-0172
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11040-024-09483-y

Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices

Author(s): Schnelli K, Xu Y.
Published in: The Annals of Applied Probability, 2023, ISSN 1050-5164
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/22-aap1826

On the operator norm of a Hermitian random matrix with correlated entries

Author(s): Reker, Jana
Published in: Random Matrices: Theory and Applications, 2022, ISSN 2010-3263
Publisher: Cornell University
DOI: 10.1142/s2010326322500368

Non–Hermitian spectral universality at critical points

Author(s): Giorgio Cipolloni, László Erdős, Hong Chang Ji
Published in: Probability Theory and Related Fields, 2025, ISSN 0178-8051
Publisher: Springer Verlag
DOI: 10.1007/s00440-025-01384-7

Optimal multi-resolvent local laws for Wigner matrices

Author(s): Cipolloni G, Erdös L, Schröder DJ
Published in: Electronic Journal of Probability, 2022, ISSN 1083-6489
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/22-ejp838

The BCS Energy Gap at High Density

Author(s): Joscha Henheik; Asbjørn Bækgaard Lauritsen
Published in: Journal of Statistical Physics, Issue 3, 2022, ISSN 0022-4715
Publisher: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10955-022-02965-9

Local stability of ground states in locally gapped and weakly interacting quantum spin systems

Author(s): Tom Wessel; Stefan Teufel; Joscha Henheik
Published in: Letters in Mathematical Physics, Issue 3, 2022, ISSN 0377-9017
Publisher: Kluwer Academic Publishers
DOI: 10.48550/arxiv.2106.13780

Density of Brown measure of free circular Brownian motion

Author(s): László Erdős, Hong Chang Ji
Published in: Documenta Mathematica, Issue 30, 2025, Page(s) 417-453, ISSN 1431-0635
Publisher: Deutsche Mathematiker-Vereinigung
DOI: 10.4171/dm/999

Creation rate of Dirac particles at a point source

Author(s): Joscha Henheik; Roderich Tumulka
Published in: Journal of Physics A: Mathematical and Theoretical, Issue 7, 2023, ISSN 1751-8113
Publisher: Institute of Physics Publishing
DOI: 10.1088/1751-8121/acfe62

Eigenstate Thermalisation Hypothesis for Translation Invariant Spin Systems

Author(s): Shoki Sugimoto; Joscha Henheik; Volodymyr Riabov; László Erdős
Published in: Journal of Statistical Physics, Issue 9, 2023, ISSN 0022-4715
Publisher: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10955-023-03132-4

Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices

Author(s): Kevin Schnelli; Yuanyuan Xu
Published in: Communications in Mathematical Physics, Issue 4, 2022, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-022-04377-y

On the Spectral Form Factor for Random Matrices

Author(s): Giorgio Cipolloni; László Erdős; Dominik Schröder
Published in: Communications in Mathematical Physics, 401 (2), 2023, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-023-04692-y

Universality in low-dimensional BCS theory

Author(s): Joscha Henheik; Asbjørn Bækgaard Lauritsen; Barbara Roos
Published in: Reviews in Mathematical Physics, 2023, ISSN 0129-055X
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0129055x2360005x

Interior-boundary conditions for the Dirac equation at point sources in three dimensions

Author(s): Henheik SJ, Tumulka R
Published in: Journal of Mathematical Physics, 2022, ISSN 0022-2488
Publisher: American Institute of Physics
DOI: 10.1063/5.0104675

Precise asymptotics for the spectral radius of a large random matrix

Author(s): Giorgio Cipolloni; László Erdős; Yuanyuan Xu
Published in: Journal of Mathematical Physics, Issue 5, 2024, ISSN 0022-2488
Publisher: American Institute of Physics
DOI: 10.1063/5.0209705

Prethermalization for Deformed Wigner Matrices

Author(s): László Erdős, Joscha Henheik, Jana Reker, Volodymyr Riabov
Published in: Annales Henri Poincaré, Issue 26, 2025, Page(s) 1991-2033, ISSN 1424-0637
Publisher: Birkhauser Verlag
DOI: 10.1007/s00023-024-01518-y

Deformational rigidity of integrable metrics on the torus

Author(s): JOSCHA HENHEIK
Published in: Ergodic Theory and Dynamical Systems, Issue 45, 2025, Page(s) 467-503, ISSN 0143-3857
Publisher: Cambridge University Press
DOI: 10.1017/etds.2024.48

Extremal statistics of quadratic forms of GOE/GUE eigenvectors

Author(s): Erdos, Laszlo; McKenna, Benjamin
Published in: Annals of Applied Probability, Issue 3, 2024, ISSN 1050-5164
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/23-aap2000

On the rightmost eigenvalue of non-Hermitian random matrices

Author(s): Cipolloni, Giorgio; Erdős, László; Schröder, Dominik; Xu, Yuanyuan
Published in: The Annals of Probability, 2023, ISSN 0091-1798
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/23-aop1643

Mesoscopic eigenvalue statistics for Wigner-type matrices

Author(s): Volodymyr Riabov
Published in: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Issue 61, 2025, ISSN 0246-0203
Publisher: Elsevier BV
DOI: 10.1214/23-aihp1438

Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap

Author(s): Henheik SJ, Teufel S.
Published in: Journal of Mathematical Physics, 2022, ISSN 0022-2488
Publisher: American Institute of Physics
DOI: 10.1063/5.0051632

Universal behavior of the BCS energy gap

Author(s): Joscha Henheik, Asbjørn Bækgaard Lauritsen
Published in: Journal of Spectral Theory, Issue 15, 2025, Page(s) 305-352, ISSN 1664-039X
Publisher: European Mathematical Society - EMS - Publishing House GmbH
DOI: 10.4171/jst/540

How a space-time singularity helps remove the ultraviolet divergence problem

Author(s): Joscha Henheik, Bipul Poudyal, Roderich Tumulka
Published in: Advances in Theoretical and Mathematical Physics, Issue 29, 2025, Page(s) 2153-2197, ISSN 1095-0761
Publisher: International Press
DOI: 10.4310/atmp.251120045919

Decorrelation transition in the Wigner minor process

Author(s): Zhigang Bao, Giorgio Cipolloni, László Erdős, Joscha Henheik, Oleksii Kolupaiev
Published in: Probability Theory and Related Fields, 2025, ISSN 0178-8051
Publisher: Springer Verlag
DOI: 10.1007/s00440-025-01422-4

Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk

Author(s): Henheik SJ, Teufel S.
Published in: Forum of Mathematics, Sigma, 2022, ISSN 2050-5094
Publisher: Cambridge University Press
DOI: 10.1017/fms.2021.80

Eigenstate Thermalization Hypothesis for Wigner-Type Matrices

Author(s): László Erdős, Volodymyr Riabov
Published in: Communications in Mathematical Physics, Issue 405, 2024, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-024-05143-y

Rank-uniform local law for Wigner matrices

Author(s): Cipolloni G, Erdös L, Schröder DJ
Published in: Forum of Mathematics, Sigma, 2022, ISSN 2050-5094
Publisher: Cambridge University Press
DOI: 10.1017/fms.2022.86

Cusp Universality for Correlated Random Matrices

Author(s): László Erdős, Joscha Henheik, Volodymyr Riabov
Published in: Communications in Mathematical Physics, Issue 406, 2025, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-025-05417-z

Directional extremal statistics for Ginibre eigenvalues

Author(s): Cipolloni G, Erdös L, Schröder DJ, Xu Y
Published in: Journal of Mathematical Physics, 2022, ISSN 0022-2488
Publisher: American Institute of Physics
DOI: 10.1063/5.0104290

The BCS Critical Temperature at High Density

Author(s): Henheik, Joscha
Published in: Mathematical Physics, Analysis, and Geometry, Issue 3, 2022, ISSN 1385-0172
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11040-021-09415-0

Functional CLT for non-Hermitian random matrices

Author(s): Erdős, László; Ji, Hong Chang
Published in: Annales de l'institut Henri Poincare (B) Probability and Statistics, Issue 7, 2023, ISSN 0246-0203
Publisher: Elsevier BV
DOI: 10.1214/22-aihp1304

Multi-point functional central limit theorem for Wigner matrices

Author(s): Jana Reker
Published in: Electronic Journal of Probability, Issue 29, 2024, ISSN 1083-6489
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/24-ejp1247

Extreme eigenvalues of Laplacian random matrices with Gaussian entries

Author(s): Andrew Campbell, Kyle Luh, Sean O’Rourke, Santiago Arenas-Velilla, Victor Perez-Abreu
Published in: Electronic Journal of Probability, Issue 30, 2025, ISSN 1083-6489
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/25-ejp1366

Mesoscopic central limit theorem for non-Hermitian random matrices

Author(s): Cipolloni, Giorgio; Erdős, László; Schröder, Dominik; id_orcid0000-0002-2904-1856
Published in: Probability Theory and Related Fields, 188 (3), Issue 15, 2024, ISSN 0178-8051
Publisher: Springer Verlag
DOI: 10.1007/s00440-023-01229-1

Functional central limit theorems for Wigner matrices

Author(s): Cipolloni G, Erdös L, Schröder DJ
Published in: Annals of Applied Probability, 2023, ISSN 1050-5164
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/22-aap1820

On adiabatic theory for extended fermionic lattice systems

Author(s): Henheik SJ, Wessel T
Published in: Journal of Mathematical Physics, 2022, ISSN 0022-2488
Publisher: American Institute of Physics
DOI: 10.1063/5.0123441

Out-of-time-ordered correlators for Wigner matrices

Author(s): Giorgio Cipolloni, László Erdős, Joscha Henheik
Published in: Advances in Theoretical and Mathematical Physics, Issue 28, 2025, Page(s) 2025-2083, ISSN 1095-0761
Publisher: International Press
DOI: 10.4310/atmp.241031013250

Local laws for multiplication of random matrices

Author(s): Ding X, Ji HC.
Published in: The Annals of Applied Probability, 2023, ISSN 1050-5164
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/22-aap1882

Central limit theorems for random matrices: From resolvents to free probability

Author(s): Reker, Jana
Published in: Issue 11, 2024
Publisher: Institute of Science and Technology Austria
DOI: 10.15479/at:ista:17164

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