The hard-core model is a basic and important model in statistical mechanics, probability, and theoretical computer science. I’ll introduce the model, and after describing some known algorithmic results, will discuss a polynomial-time algorithm for approximately sampling from the hard-core model at high densities on the integer lattices. This is the regime in which the Glauber dynamics are known to mix exponentially slowly. Our algorithm relies in an essential way on Pirogov-Sinai theory, an important tool for understanding the phase diagram of high-density discrete statistical mechanics models.

This is joint work with Will Perkins and Guus Regts.

**Date**: 12 November 2018, 12:00 (Monday, 6th week, Michaelmas 2018)**Venue**: L4**Speaker**: Tyler Helmuth (University of Bristol)**Organising department**: Department of Statistics**Organisers**: Christina Goldschmidt (Department of Statistics, University of Oxford), James Martin (Department of Statistics, University of Oxford)**Part of**: Probability seminar**Booking required?**: Not required**Audience**: Public- Editor: Christina Goldschmidt