Lyapunov exponents: recent applications of Furstenberg's theorem in
spectral theory
February 20, 2019
3:00 pm PHG 646
Abstract
In this talk we describe a new proof of a classical result and a
number of new results that can be proved along similar lines. At the
heart of this approach are the verification of the assumptions of
Furstenberg's theorem about products of random matrices and a way to
parlay the output of this theorem via large deviation estimates into
statements commonly referred to as "Anderson localization."
The various settings we consider include quantum evolution in random
environments and orthogonal polynomials on the unit circle with random
recursion parameters.
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