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The Zigzag Strategy for Random Band Matrices
Mathematical Physics Seminar| Speaker: | Vova Riabov, IST Austria |
| Related Webpage: | https://sites.google.com/view/volodymyr-riabov |
| Location: | 2112 MSB |
| Start time: | Thu, Sep 25 2025, 11:00AM |
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.
Joint seminar with Probability