#### Mathematical Physics Seminar - Antti Knowles, Courant Institute - Quantum diffusion and delocalization for random band matrices

I give a summary of recent progress in establishing the diffusion approximation for random band matrices. We obtain a rigorous derivation of the diffusion profile in the regime W > N^{4/5}, where W is the band width and N the dimension of the matrix. As a corollary, we prove complete delocalization of the eigenvectors. Our proof is based on a new self-consistent equation for the Green function.

Joint work with L. Erdos, H.T. Yau, and J. Yin.

**Location:**
Jadwin A06

**Date/Time: **03/05/13
at
4:30 pm
- 03/05/13
at
6:00 pm

**Category: **Mathematical Physics Seminar

**Department: **Physics