Abstract:
We study forest fire processes on a two-dimensional lattice: all vertices are initially vacant, and then become occupied at rate 1. If an occupied vertex is hit by lightning, which occurs at a (typically very small) rate, its entire occupied cluster burns immediately, i.e. all its vertices become vacant. In particular, we want to analyze the near-critical behavior of such processes, that is, when large connected components of occupied sites start to appear. For that, we develop a substantial generalization of near-critical percolation to a lattice containing "impurities" (left by the successive fires). These impurities are not only microscopic, but also allowed to be "mesoscopic'', which makes the proofs quite delicate. This talk is based on a joint work with Rob van den Berg (CWI and VU, Amsterdam).
Biography:
Pierre Nolin is an Associate Professor at City University of Hong Kong. He received his Ph.D. 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