Percolation of random nodal lines (Vincent Beffara, Institut Fourier in Grenoble, France)

24.10.2016 15:15 – 17:15

We prove a Russo-Seymour-Welsch percolation theorem for nodal domains and nodal lines associated to a natural infinite dimensional space of real analytic functions on the real plane. More precisely, let U be a smooth connected bounded open set in R^2 and \gamma, \gamma' two disjoint arcs of positive length in the boundary of U. We prove that there exists a positive constant c, such that for any positive scale s, with probability at least c there exists a connected component of \{x \in U, f(sx) > 0 \} intersecting both \gamma and \gamma′, where f is a random analytic function in the Wiener space associated to the real Bargmann-Fock space. For s large enough, the same conclusion holds for the zero set \{ x \in U, f(sx) = 0 \}. As an important intermediate result, we prove that sign percolation for a general stationary Gaussian field can be made equivalent to a correlated percolation model on a lattice. [Joint work with Damien Gayet.]

Lieu

Room 623 15:15-16:00 & Room 17 16:30-17:15, Séminaire "Mathématique Physique"

entrée libre