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

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

preprint2011arXivOpen access
Jean-Marc AzaïsMario Wschebor
math.PR
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Jean-Marc AzaïsMario Wschebor

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