The Zigzag Strategy for Random Band MatricesOberseminar Stochastics

by Volodymyr (Vova) Riabov (Institute of Science and Technology Austria)

Thursday Nov 27, 2025, 4:30 PM → 5:30 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

Random band matrices have entries concentrated in a narrow band of width
W around the main diagonal, modeling systems with spatially localized in-
teractions. We consider one-dimensional random band matrices with band-
width W ≫ N 1/2, general variance profile, and arbitrary entry distributions.
We establish complete isotropic delocalization, quantum unique ergodicity
(eigenstate thermalization), and Wigner-Dyson universality in the bulk of the
spectrum. The key technical input is a family of local laws capturing the spa-
tial decay of resolvent entries, established using a combination of Ornstein-
Uhlenbeck dynamics and Green function comparison (the Zigzag strategy).
Based on joint work with  Laszló Erdős.