Student Probability and Mathematical Physics Seminar

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Harmonic analysis of Gaussian multiplicative chaos on the unit circle

Speaker: Emmy Li, CIMS

Location: Warren Weaver Hall 202

Date: Tuesday, November 25, 2025, 12:30 p.m.

Synopsis:

Given a Radon measure on the unit circle $[0,2\pi)$, it is often difficult to understand the asymptotic behaviour of its Fourier coefficients, especially when the measure is supported on a fractal set. A measure is called a \emph{Rajchman measure} if its Fourier coefficients $c_n$ tend to $0$ as $|n|\to\infty$. In this talk I will present the approach of Garban and Vargas, who prove that Gaussian multiplicative chaos on the circle is almost surely a Rajchman measure. I will also discuss some of the interesting ideas behind the convergence in law result.