# Applied Mathematics Colloquium: Dr. Patrick Lopatto

## Brown University

Friday, March 18, 2022

2:00 PM – 3:00 PM

2:00 PM – 3:00 PM

Title: Fluctuations in local quantum unique ergodicity for generalized Wigner matrices

Abstract: I will discuss some recent results on the structure of eigenvectors of random matrices. These include optimal delocalization estimates, the equidistribution of eigenvector entries on all scales (known as quantum unique ergodicity), and the convergence of the fluctuations around local equidistribution. The proofs are dynamical and rely on a study of the eigenvector moment flow, which describes the evolution of eigenvector observables under Dyson Brownian motion. This is joint work with Lucas Benigni.

Abstract: I will discuss some recent results on the structure of eigenvectors of random matrices. These include optimal delocalization estimates, the equidistribution of eigenvector entries on all scales (known as quantum unique ergodicity), and the convergence of the fluctuations around local equidistribution. The proofs are dynamical and rely on a study of the eigenvector moment flow, which describes the evolution of eigenvector observables under Dyson Brownian motion. This is joint work with Lucas Benigni.

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