We prove that the eigenvectors of Wigner matrices satisfy the Eigenstate Thermalization 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 a Wigner matrix analog of the Berry random wave conjecture.
org: CAPUTO Pietro