Abstract:
The Fourier coefficients of multiplicative chaos measures appear naturally in the study of random matrices, QFTs, and even number theory. The harmonic analysis of the canonical GMC measure on the unit circle allowed Garban and Vargas to show that the associated Fourier coefficients tend to 0. The next step is to ask how fast this decay occurs, which corresponds to the Fourier dimension studied in fractal analysis. We compute the exact Fourier dimension of the circle-GMC measure (and many more), thereby proving a conjecture of Garban-Vargas based on a fourth moment computation. Our arguments are elementary, relying on a construction of an auxiliary, scale-invariant Gaussian field.
Biography:
William Verreault is a PhD student and Vanier Scholar at the University of Toronto, advised by Ilia Binder. His research is in analysis and probability. His research program aims to get a better understanding of lattice models in statistical physics and their connections with complex analysis, function spaces, and random matrix theory. In particular, he is interested in SLE, the GFF, and GMC, and their interactions with random geometry and conformal field theory.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.