The Zigzag Strategy for Random Band Matrices
Budapest-Vienna Probability Seminar
Date
Friday, October 10, 2025 16:30 - 17:20
Speaker
Volodymyr Riabov (ISTA)
Location
Central Bldg / O1 / Mondi 2a (I01.O1.008)
Series
Seminar/Talk
Tags
mathematical_seminar_ics
Host
Laszlo Erdös, Jan Maas
Contact
Random band matrices have entries concentrated in a narrow band of width W around the main diagonal, modeling systems with spatially localized interactions. We consider one-dimensional random band matrices with bandwidth W >> N^, 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 spatial decay of resolvent entries, established using a combination of Ornstein-Uhlenbeck dynamics and Green function comparison (the Zigzag strategy). Based on joint work with Lszl Erds.