Diane Holcomb: On the centered maximum of the Sine beta process

Abstract: There has been a great deal or recent work on the asypmtotics of the maximumof characteristic polynomials or random matrices. Other recent work studies the analogous result for log-correlated Gaussian fields. Here we will discuss a maximumresult for the centered counting function of the Sine beta process. The Sine beta process arises as the local limit in the bulk of a beta-ensemble, and was originally described as the limit of a generalization of the Gaussian Unitary Ensemble by Valko and Virag with an equivalent process identified as a limit of the circular beta ensembles by Killip and Stoiciu. A brief introduction to the Sine process as well as some ideas from the proof of themaximum will be covered. This talk is on joint work with Elliot Paquette.