Student Probability Seminar

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Random matrices and GMC

Speaker: Ahmet Keles, CIMS

Location: Warren Weaver Hall 1314

Date: Monday, April 14, 2025, 11 a.m.

Synopsis:

We will discuss an alternative proof of a result by Berestycki, Webb, and Wong (2018) and Charlier (2019) in a simple setting, showing that the powers of the absolute value of the characteristic polynomial of the Gaussian Unitary Ensemble (GUE) converge to a Gaussian multiplicative chaos (GMC) measure, under suitable normalization. The proof follows the probabilistic framework introduced by Bourgade and Falconet (2022), and is based on the loop equation technique from Johansson (1998) along with the determinantal point process structure of the eigenvalues of GUE. We will also discuss the strengths and limitations of this method, particularly in view of potential generalizations beyond the GUE setting.