Universality phenomena for random matrices

03.05.2023 15:15 - 16:15

László Erdös (IST Austria)

Abstract: Large random matrices tend to exhibit universal fluctuations. Beyond the well-known Wigner-Dyson and Tracy-Widom eigenvalue distributions, we overview other universality results for Hermitian and non-Hermitian matrices. We discuss the emergence of normal distribution involving eigenvectors, especially the random matrix version of quantum unique ergodicity. We also explain why results on non-Hermitian random matrices are much harder than their Hermitian counterparts and highlight our new methods to tackle them.

R.I. Bot, A. Mellit, J.L. Romero

Sky Lounge, 12. OG, OMP 1