Perturbation Theory for Band Matrices

Topic:Perturbation Theory for Band Matrices
Speaker:Sasha Sodin
Affiliation:Member, School of Mathematics
Date:Friday, November 19
Time/Room:2:00pm - 3:00pm/S-101

Band matrices are a class of random operators with rows and columns indexed by elements of the d-dimensional lattice, and random entries H(u, v) which are small when the distance between u and v on the lattice is larger than W. We shall discuss the spectral properties of these matrices for large W. In particular, we shall try to explain how a perturbation expansion can be applied at the edge of the spectrum, and why does the analogous series for the bulk of the spectrum diverge. Time permitting, we shall introduce a regularisation procedure which may help improve the convergence.