Bálint Virág: How noisy is a rough string?

Speaker: Bálint Virág

Title:  How noisy is a rough string?

Abstract: Modify the graph of the integers Z so that each vertex gets a loop of weight epsilon with probability half independently.   This is called the 1-dimensional Bernoulli-Anderson model.   It is a long-standing open problem whether the expected spectral measure of this weighted graph is absolutely continuous for small enough epsilon.   I will talk about a result with my former PhD student, Eric Hart, showing that this measure is Holder with exponent 1-c epsilon. This improves on previous results of Bourgain using new methods.