Recursions and tightness for the maximum of the discrete, two\n dimensional Gaussian Free Field

2010/05/28 by Erwin Bolthausen, Bolthausen, Erwin, Jean‐Dominique Deuschel +4 · 1 citation
Computer Science · Mathematics · #60G15 #60J80 #Bayesian Methods and Mixture Models #Data Management and Algorithms #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1005.5417

openalex publication_date 2010/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the maximum of the discrete two dimensional Gaussian free field\nin a box, and prove the existence of a (dense) deterministic subsequence along\nwhich the maximum, centered at its mean, is tight; this still leaves open the\nconjecture that tightness holds without the need for subsequences. The method\nof proof relies on an argument developed by Dekking and Host for branching\nrandom walks with bounded increments and on comparison results specific to\nGaussian fields.\n

Citations

• Chaos, concentration, and multiple valleys

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• Branching Brownian motion with selection of the N right-most particles:\n An approximate model

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