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Probability and Combinatorics

Tuesday, January 25, 2022 - 3:30pm

Giorgio Cipolloni



University of Pennsylvania

David Rittenhouse Lab 4C8

We prove that the eigenvectors of Wigner matrices satisfy the Eigenstate Thermalisation Hypothesis (ETH), which is a strong form of Quantum Unique Ergodicity (QUE) with optimal speed of convergence. Then, using this a priori bound as an input, we analyze the stochastic Eigenstate Equation (SEE) and prove Gaussian fluctuations in the QUE. The main methods behind the above results are: (i) multi-resolvents local laws established via a novel bootstrap scheme; (ii) energy estimates for SEE.