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Eigenstate thermalisation hypothesis and functional CLT for Wigner matrices

  • Laszlo Erdös
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Abstract

We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix W with an optimal error inversely proportional to the square root of the dimension. This verifies a strong form of Quantum Unique Ergodicity with an optimal convergence rate and we also prove Gaussian fluctuations around this convergence after a small spectral averaging. This requires to extend the classical CLT for linear eigenvalue statistics, Tr f(W), to include a deterministic matrix A and we identify three different modes of fluctuation for Tr f(W)A in the entire mesoscpic regime. The key technical tool is a new multi-resolvent local law for Wigner ensemble.

seminar
7/9/20 3/9/23

Webinar Analysis, Quantum Fields & Probability

MPI for Mathematics in the Sciences Live Stream

Jochen Zahn

Leipzig University Contact via Mail

Roland Bauerschmidt

University of Cambridge

Stefan Hollands

Leipzig University & MPI MiS Leipzig

Christoph Kopper

Ecole Polytechnique Paris

Antti Kupiainen

University of Helsinki

Felix Otto

MPI for Mathematics in the Sciences Contact via Mail

Manfred Salmhofer

Heidelberg University