Notice
Percolation of random fields excursions
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Descriptif
We consider homogeneous real random functions defined on the Euclidean space. We are in particular interested in the percolation properties of their excursion sets in dimension 2, defined as the (random) sets obtained after thresholding the field at some fixed value which is the parameter. We will present some results obtained for 1- centred Gaussian random fields and 2- for shot-noise fields, which can be seen as the Poisson counterparts of Gaussian fields. It turns out that under mild assumptions, as in many parametric models, there is a critical value that separates percolation from non-percolation, and we furthermore observe a sharp phase transition around this value. For symmetric auto-dual models, and in particular for Gaussian excursions, the critical value is trivially 0. For non-symmetric shot-noise excursions, we estimate the critical value at high intensity by approximating the shot-noise field by a Gaussian field through a strong invariance principle.
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