The seminar is sponsored by NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai.
Abstract:
Motivated by the issue of "persistence" of percolation in systems of layered horizontal one-dimensional long range "critical" bond percolation, with the addition of vertical nearest neighbor bonds, we introduce a percolation system of layered renewal intervals: each horizontal layer is partitioned in intervals according to a renewal process with a inter-renewal distribution given by a random variable T. Between each pair of layers we place vertical segments according to a Poisson process of rate epsilon. A site inoa layer is said to percolate if there exists an infinite path starting starting at that site going through horizontal intervals and vertical segments, not crossing renewal points. We are interested on conditions over the distribution of T insuring either that the origin percolates with positive probability for every epsilon>0 or that there exists a positive threshold for epsilon below which the origin does not percolate almost surely. This is an ongoing joint project with Maria Eulália Vares and Domingos Marchetti. Time allowing, related issues and results for a 2d Ising model version of those models with a Kac potential in the horizontal direction will be mentioned. These are based on joint work with also Titti Merola and Errico Presutti.
Biography:
Luiz Renato Fontes is Visiting Professor of Mathematics at NYU Shanghai. He is also Professor at the Instituto de Matemática e Estatística, Universidade de São Paulo, Brasil. His research interests are Probability Theory, Stochastic Processes and Random Media.