Event time:
Wednesday, September 17, 2025 - 4:00pm
Location:
KT 101
Speaker:
Vova Riabov
Speaker affiliation:
IST Austria - Future University Hakodate, Japan
Event description:
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^½, 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 László Erdős.