Speaker: 

William Wood

Institution: 

UC Irvine

Time: 

Tuesday, October 11, 2022 - 1:00pm to 2:00pm

Location: 

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, which claims that a Schrodinger cocycle is uniformly hyperbolic if and only if the corresponding energy value is not in the almost sure 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. A period 3 model, given specific conditions, can have infinitely many intervals in the spectrum, however.