ERC Starting Grant · 2016
Spectral Statistics of Structured Random Matrices
The purpose of this proposal is a better mathematical understanding of certain classes of large random matrices. Up to very recently, random matrix theory has been mainly focused on mean-field models with independent entries. In this proposal I instead consider random matrices that incorporate some nontrivial structure. I focus on two types of structured random matrices that arise naturally in important applications and lead to a rich mathematical behaviour: (1) random graphs with fixed degrees, such as random regular graphs, and (2) random band matrices, which constitute a good model of disordered quantum Hamiltonians. The goals are strongly motivated by the applications to spectral graph…
From the public funding record at EU CORDIS. Describes the funded project, not the reviews below.