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Poisson-Dirichlet Statistics for the extremes of the two-dimensional discrete Gaussian free field

By Louis-Pierre Arguin and Olivier Zindy

Abstract

International audienceIn a previous paper, the authors introduced an approach to prove that the statistics of the extremes of a log-correlated Gaussian field converge to a Poisson-Dirichlet variable at the level of the Gibbs measure at low temperature and under suitable test functions.The method is based on showing that the model admits a one-step replica symmetry breaking in spin glass terminology.This implies Poisson-Dirichlet statistics by general spin glass arguments.In this note, this approach is used to prove Poisson-Dirichlet statistics for the two-dimensional discrete Gaussian free field, where boundary effects demand a more delicate analysis

Topics: Gaussian free field, Gibbs measure, Poisson-Dirichlet variable, [ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST]
Publisher: Institute of Mathematical Statistics (IMS)
Year: 2015
DOI identifier: 10.1214/EJP.v20-3077
OAI identifier: oai:HAL:hal-01214647v1
Provided by: Hal-Diderot

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