We show that the existence of a" good"'coupling wrt Hamming distance for any local Markov
chain on a discrete product space implies rapid mixing of the Glauber dynamics in a …

A well-known conjecture in computer science and statistical physics is that Glauber
dynamics on the set of k-colorings of a graph G on n vertices with maximum degree Δ is …

In recent years there has been considerable progress on the analysis of Markov chains for
generating a random coloring of an input graph. These improvements have come in …

This thesis explores proofs by coupling from the perspective of formal verification. Long
employed in probability theory and theoretical computer science, these proofs construct …

We study a simple Markov chain, known as the Glauber dynamics, for generating a random
k‐coloring of an n‐vertex graph with maximum degree Δ. We prove that, for every ε> 0, the …

We study a simple Markov chain, known as the Glauber dynamics, for generating a random
k-coloring of a n-vertex graph with maximum degree/spl Delta/. We prove that the dynamics …

Determining the mixing time of Kac's random walk on the sphere S^n-1 is a long-standing
open problem. We show that the total variation mixing time of Kac's walk on S^n-1 is …

We analyse the mixing time of Markov chains using path coupling with stopping times. We
apply this approach to two hypergraph problems. We show that the Glauber dynamics for …

We introduce a versatile technique called spectral independence for the analysis of Markov
chain Monte Carlo algorithms in high-dimensional probability and statistics. We rigorously …

In this paper we examine the importance of the choice of metric in path coupling, and its
relationship to stopping time analysis. We give strong evidence that stopping time analysis is …