On the size of level-set components for strongly correlated Gaussian fields

17.04.2023 16:15

We study the level-sets of smooth Gaussian fields on R^d with slow decay of correlations (i.e. algebraic decay with exponent smaller than 1). As the level varies, this defines a percolation model, for which we compute the exact exponential rate of decay in probability for the size of subcritical connected components. This rate turns out to be proportional to the inverse correlation times the square of the distance to the critical level. This differs drastically from fields with fast decay of correlations, for which the cluster size probability always decays exponentially, and the precise rate constant is not well understood. Our result is an evidence in support of physicists' predictions for the characteristic length exponent of fields with slow algebraic decay of correlations, and also opens to way to the study of other large deviations questions for smooth Gaussian fields. In this talk, I aim at explaining how the existence of strong correlations leads to a (perhaps surprisingly) better understanding of these large deviation questions. This is based on a joint work with Stephen Muirhead.

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Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Mathématique Physique"

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