The tail of the maximum of smooth Gaussian fields on fractal sets

2011/09/18 by Jean‐Marc Azäis, Azaïs, Jean-Marc, Mario Wschebor +1
Mathematics · #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.1109.3895

openalex publication_date 2011/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the probability distribution of the maximum M_S of a smooth stationary Gaussian field defined on a fractal subset S of \Rⁿ. Our main result is the equivalent of the asymptotic behavior of the tail of the distribution ¶(M_S>u) as u→ +∞. The basic tool is Rice formula for the moments of the number of local maxima of a random field.

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