Eigenstate thermalisation hypothesis and functional CLT for Wigner matrices

  • Laszlo Erdös
Live Stream


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.

09.07.20 09.03.23

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