2013/10/08 by Louis‐Pierre Arguin, Arguin, Louis-Pierre, Olivier Zindy +1
Environmental Science · Mathematics · Physics and Astronomy · #60F05 #60G70 #82B26 #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Mathematics #FOS: Physical sciences #Plant Water Relations and Carbon Dynamics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #primary 60G15 #secondary 82B44
paper · doi:10.48550/arxiv.1310.2159
openalex publication_date 2013/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 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.