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Franco Severo

On the size of subcritical level-set components for strongly correlated Gaussian fields
Mardi, 11 Octobre, 2022 - 14:00 à 15:00
Résumé : 

Consider the level-sets of smooth Gaussian fields on the d-dimensional Euclidean space, which defines a percolation model undergoing a non-trivial phase transition. Assuming that the field has a slow decay of correlations, we compute the exact exponential rate of decay for the size of subcritical connected components, which is proportional to the inverse correlation times the square of the distance to criticality. This differs drastically from fields with fast decay of correlations, for which the cluster size always decays exponentially, and the precise rate constant is not well understood. Our result is an evidence in support of physicists' predictions of the correlation length exponent for fields with slow algebraic decay of correlations, and also opens to way to the study of other large deviations questions in Gaussian percolation. 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. Based on a joint work with Stephen Muirhead.

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