Extreme values for two-dimensional discrete Gaussian free field

2012/06/02 by Jian Ding, Ding, Jian, Ofer Zeitouni +1 · 2 citations
Economics, Econometrics and Finance · Mathematics · #60G15 #60G60 #60G70 #FOS: Mathematics #Geometry and complex manifolds #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1206.0346

openalex publication_date 2012/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider in this paper the collection of near maxima of the discrete, two dimensional Gaussian free field in a box with Dirichlet boundary conditions. We provide a rough description of the geometry of the set of near maxima, estimates on the gap between the two largest maxima, and an estimate for the right tail up to a multiplicative constant on the law of the centered maximum.

Cited by

• Poisson-Dirichlet Statistics for the extremes of the two-dimensional discrete Gaussian Free Field
• Full extremal process in four-dimensional membrane model

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