Tightness of the recentered maximum of log-correlated Gaussian fields

2013/11/08 by Javier Acosta, Acosta, Javier · 1 citation
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1311.2000

openalex publication_date 2013/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a family of centered Gaussian fields on the d-dimensional unit box, whose covariance decreases logarithmically in the distance between points. We prove tightness of the recentered maximum of the Gaussian fields and provide exponentially decaying bounds on the right and left tails. We then apply this result to a version of the two-dimensional continuous Gaussian free field.

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