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

Time: Tue 2018-03-20 15.15 - 16.16

Location: Room F11, KTH

Participating: Diane Holcomb, KTH

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Abstract: There has been a great deal or recent work on the asypmtotics of the maximum of characteristic polynomials or random matrices. Other recent work studies the analogous result for log-correlated Gaussian fields. Here we will discuss a maximum result 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 the maximum will be covered.