Eigenstate thermalisation hypothesis and Gaussian fluctuations 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. The key technical tool is a new multi-resolvent local law for Wigner ensemble and the Dyson Brownian motion for eigenvector overlaps.
mathematical physics
Audience: researchers in the discipline
( video )
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Organizers: | Margherita Disertori*, Wojciech Dybalski*, Ian Jauslin, Hal Tasaki* |
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