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We prove the Eigenstate Thermalisation Hypothesis for Wigner matrices uniformly in the entire spectrum, in particular near the spectral edges, with a bound on the fluctuation that is optimal for any observable.
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L. Erdős, A. Knowles, H.-T. Yau, J. Yin. The local semicircle law for a general class of random matrices. Electronic Journal of Probability
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A. Knowles, J. Yin. The isotropic semicircle law and deformation of Wigner matrices. Communications on Pure and Applied Mathematics 66
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A. Bloemendal, L. Erdős, A. Knowles, H.-T. Yau, J. Yin. Isotropic local laws for sample covariance and generalized Wigner matrices. Electronic Journal of Probability 19
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A. Adhikari, B. Landon. Local law and rigidity for unitary Brownian motion. arXiv: 2202.06714 (2022)
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L. Benigni, P. Lopatto. Optimal delocalization for generalized Wigner matrices. Advances in Mathematics 396
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2017
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N. Cook, W. Hachem, J. Najim, D. Renfrew. Non-Hermitian random matrices with a variance profile (I): deterministic equivalents and limiting ESDs. Electronic Journal of Probability 23
2018
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O.H. Ajanki, L. Erdős, T. Krüger. Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields 173
2019
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L. Erdős, T. Krüger, D. Schröder. Random matrices with slow correlation decay. Forum of Mathematics, Sigma 7
2019
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2020
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2022
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G. Cipolloni, L. Erdős, D. Schröder. Normal fluctuation in quantum ergodicity for Wigner matrices. The Annals of Probability 50
2022
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G. Cipolloni, L. Erdős, D. Schröder. Thermalisation for Wigner matrices. Journal of Functional Analysis 282
2022
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G. Cipolloni, L. Erdős, D. Schröder. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability 27
2022
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G. Cipolloni, L. Erdős, D. Schröder. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma 10
2022
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G. Cipolloni, L. Erdős, J. Henheik, O. Kolupaiev. Gaussian fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma 11
2023
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