Eigenstate thermalisation hypothesis and functional CLT for Wigner matrices

Laszlo Erdös (IST Austria)

11-Feb-2021, 16:00-17:30 (3 years ago)

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.

statistical mechanicsmathematical physicsanalysis of PDEsprobability

Audience: researchers in the topic


Analysis, Quantum Fields, and Probability

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Recorded talk are available on youtube.

Organizers: Roland Bauerschmidt, Stefan Hollands, Christoph Kopper, Antti Kupiainen, Felix Otto, Manfred Salmhofer
Curator: Jochen Zahn*
*contact for this listing

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