Asymptotics of Toeplitz determinants with Fisher-Hartwig singularities and applications to random matrix theory

22 October 2019
15:30
Benjamin Fahs
Abstract

We discuss asymptotics of Toeplitz determinants with Fisher--Hartwig singularities, and give an overview of past and more recent results.
Applications include the study of asymptotics of certain statistics of the characteristic polynomial of the Circular Unitary Ensemble (CUE) of random matrices. In particular recent results in the study of Toeplitz determinants allow for a proof of a conjecture by Fyodorov and Keating on moments of averages of the characteristic polynomial of the CUE.
 

  • Random Matrix Theory Seminars