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Title:
Eigenstate thermalisation hypothesis and Gaussian fluctuations for Wigner matrices

Speaker:
Laszlo Erdos

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.

Link:
https://www.msri.org/workshops/947/schedules/30257

Workshop:
MSRI- [HYBRID WORKSHOP] Connections and Introductory Workshop: Universality and Integrability in Random Matrix Theory and Interacting Particle Systems, Part 1