Abstract:
Bernoulli percolation is a model for random media introduced by Broadbent and Hammersley in 1957. In this process, each vertex of a given graph is occupied or vacant, with respective probabilities p and 1-p, independently of the other vertices (for some parameter p). It is arguably one of the simplest models from statistical mechanics displaying a phase transition as the parameter p varies, i.e. a drastic change of behavior at some critical value p_c, and it has been widely studied.
Benjamini and Kesten introduced in 1995 the problem of embedding infinite binary sequences into a Bernoulli percolation configuration, known as percolation of words. We give a positive answer to their Open Problem 2: for percolation on Z^3 with parameter p=1/2, we prove that almost surely, all words can be embedded. We also discuss various extensions of this result. This talk is based on a joint work with Augusto Teixeira (IMPA) and Vincent Tassion (ETH Zürich).
Biography:
Pierre Nolin is an Associate Professor at City University of Hong Kong. He received his PhD from Université Paris-Sud 11 and École Normale Supérieure in 2008. Before moving to Hong Kong in 2017, he worked as an Instructor and PIRE fellow at the Courant Institute (NYU), and then as an Assistant Professor at ETH Zürich. His research is focused on probability theory and stochastic processes, in connection with questions originating from statistical mechanics. He is particularly interested in lattice models such as the Ising model of ferromagnetism, Bernoulli percolation, Fortuin-Kasteleyn percolation, frozen percolation, and forest fire processes.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai