William Wood


UC Irvine


Tuesday, May 10, 2022 - 1:00pm to 2:00pm


RH 440R

In this talk we will focus on the notion of uniform hyperbolicity of sets of matrices, and apply it to transfer matrices related to a discrete Schrodinger operator to study its spectrum. Specifically, we will show how to apply Johnson’s Theorem that claims that a Schrodinger cocycle is uniformly hyperbolic if and only if the corresponding energy value is not in the spectrum, to the periodic Anderson-Bernoulli Model. As a result, we will prove that the spectrum of period two Anderson-Bernoulli Model consists of at most four intervals.