Zigzag strategy for Wigner matrices

Vienna Probability Seminar

Over the past years, so called multi-resolvent local laws (= strong concentration estimates for alternating products of random resolvents and deterministic matrices) emerged as a powerful tool for tackling several questions in random matrix theory. In this talk, we will explain a novel dynamical method, the Zigzag strategy, for proving these estimates in the simplest case of Wigner matrices. The key idea behind the Zigzag strategy is a tandem of the characteristic flow method and a self-consistent Green function comparison (GFT) argument. Joint work with Giorgio Cipolloni and Laszlo Erds.