### Diffusion profile and delocalization for random band matrices

**Knowles, A ***(New York University)*

Wednesday 19 September 2012, 11:10-11:50

Seminar Room 1, Newton Institute

#### Abstract

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.

#### Presentation