Graduate Student / Postdoc Seminar

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Extremal Processes for Some Gaussian Random Fields

Speaker: Ofer Zeitouni

Location: Warren Weaver Hall 1302

Date: Friday, October 23, 2015, 1 p.m.

Synopsis:

Consider a (locally finite) random configuration \({\bf X}=\{X_i\}\) with values in \(R\) (such a collection is called a point process). Let \(Z_i\) be i.i.d. random variables, independent of \({\bf X}\). Assume that the distribution of \({\bf X}\) is invariant under the transformation \(X_i\mapsto X_i+Z_i\). Liggett has identified all possible such distributions, as mixtures of Poisson processes with (constant or exponential) intensities. Recently, this identification has played an important role in identifying the point process of extremes of certain Gaussian random fields. I will describe Liggett's results and explain how it is applied to the study of such extremes, as well as applications to the study of the Gaussian free field and to certain spin-glass systems. All terms will be defined in the talk.