Mini-course: Introduction to Percolation Theory and related Processes

Time:09:30:02/05/2019 to  11:45:03/05/2019

Venue/Location: C2-714, VIASM

Speaker: Assoc. Prof. Pierre Nolin – City University of Hong Kong


In this mini-course, we give a detailed introduction to percolation theory. Bernoulli percolation is obtained by deleting at random, independently, the edges (or the vertices) of a given lattice. It is arguably one of the simplest models from statistical mechanics that displays a phase transition, i.e. a drastic change of macroscopic behavior at a certain critical threshold. We present the main tools and techniques used to study percolation, as well as the most important results.

We then discuss forest fire (or epidemics) processes, which are models of "activated media" first considered in statistical physics. On a two-dimensional lattice, all vertices are initially vacant, and then become occupied at some given (fixed) rate 1. If an occupied vertex is hit by lightning, which occurs at a very small rate, all the occupied vertices connected to it burn, i.e. become vacant. Many questions remain open about the long-time behavior of such processes. In particular, we want to explain why the "near-critical" regime of Bernoulli percolation arises naturally.

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.