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

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

2011-09-18

arxiv.org/abs/1109.3895v1

Mathematics

Probability

Scientific paper

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 $\P(M_S>u)$ as $u\rightarrow +\infty.$ The basic tool is Rice
formula for the moments of the number of local maxima of a random field.

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