Michael Hofstetter - Extreme values of the sine-Gordon field
|Starts:||15:00 8 Dec 2021|
|Ends:||16:00 8 Dec 2021|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
Michael Hofstetter (University of Cambridge) will speak in the Probability seminar.
In recent years there has been significant progress in the study of extreme values of log-correlated Gaussian fields, in particular in that of the Gaussian free field, thanks to the work of Bramson, Ding, Roy, Zeitouni and Biskup, Louidor.
In these works, it has been shown that for the discrete Gaussian free field (DGFF) in d=2 the limiting law of the collection of all local maxima of the field (called the extremal process) is a Poisson process with a random intensity measure.
In this talk I will explain how an analogous result is obtained for the non-Gaussian sine-Gordon field. I will present a strong coupling at all scales of the sine-Gordon field with the Gaussian free field and demonstrate how this can be used to extend existing methods for the maximum and the extremal process of the DGFF. The talk is based on a joint work with R. Bauerschmidt.
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