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The percolation phase transition of the random plane wave

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Speaker: Hugo Vanneuville from Université Grenoble-Alpes
Event date: Thursday, 06 May 2021 01:00 pm - Tuesday, 19 January 2038 04:14 am
Place: WEBEX

Abstract: Consider the random plane wave f, which is a random eigenfunction of the Laplacian in \R^2. Given a real number u, we study the connectivity properties of the set {f<u}, and we show that the model undergoes a percolation phase transition at u=0: if u<0 then a.s. there is no unbounded connected component in {f<u} while this is a.s. the case if u>0. As I will explain in the talk, the main difficulty is that the field is not positively correlated. In the talk, I will present the strategy of proof, based on some superconcentration considerations that have enabled us to revisit the following general idea from (Russo, 1982; Talagrand, 1994...): "an event satisfies a phase transition if it depends little on any given point". This is joint work with Stephen Muirhead and Alejandro Rivera

Webex meeting information:


Thursday, May 6, 2021 1:00 pm | 1 hour | (UTC+02:00) Amsterdam, Berlin, Bern, Rome, Stockholm, Vienna

Meeting number: 163 304 7008

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