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Title:
Perturbation Theory for Band Matrices
Speaker:
Abstract:
ANALYSIS/MATHEMATICAL PHYSICS SEMINAR
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.
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