Abstract:
Bernoulli percolation can be used to analyze planar forest fire (or epidemics) processes. In such processes, all vertices of a lattice 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, all the vertices connected to it burn immediately, i.e. they become vacant.
We want to analyze the behavior of such processes near and beyond criticality, that is, when large components of occupied sites appear. They display a form of self-organized criticality, where the phase transition of Bernoulli percolation plays an important role. In particular, a peculiar and striking phenomenon arises, that we call "near-critical avalanches".
This talk is based on joint works with Rob van den Berg (CWI and VU, Amsterdam) and with Wai-Kit Lam (National Taiwan University, Taipei).
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
This event is open to the NYU Shanghai community and Math community.