Eigenstate thermalisation hypothesis and functional CLT for Wigner matrices
Laszlo Erdös (IST Austria)
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
Series comments: Please register for the newsletter mailing list to receive information on upcoming webinars and for zoom login details.
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 |