Rapid mixing of subset Glauber dynamics on graphs of bounded tree-width

TL;DR

This paper introduces a general method to analyze the rapid mixing of Glauber dynamics for certain graph polynomials on graphs with bounded tree-width, extending previous results to new classes of polynomials.

Contribution

The authors develop a unified approach based on subset expansion and canonical paths to prove rapid mixing for Glauber dynamics on graphs of bounded tree-width for multiple graph polynomials.

Findings

Chains mix rapidly on graphs of bounded tree-width

Extends rapid mixing results to Tutte, adjacency-rank, and interlace polynomials

Provides a general framework for analyzing Glauber dynamics

Abstract

Motivated by the `subgraphs world' view of the ferromagnetic Ising model, we develop a general approach to studying mixing times of Glauber dynamics based on subset expansion expressions for a class of graph polynomials. With a canonical paths argument, we demonstrate that the chains defined within this framework mix rapidly upon graphs of bounded tree-width. This extends known results on rapid mixing for the Tutte polynomial, the adjacency-rank ($R_2$-)polynomial and the interlace polynomial.