We extend the notion of spectral independence (introduced by Anari, Liu, and Oveis
Gharan) from the Boolean domain to general discrete domains. This property characterises …

The spectral independence approach of Anari et al.(2020) utilized recent results on high-
dimensional expanders of Alev and Lau (2020) and established rapid mixing of the Glauber …

Strong spatial mixing (SSM) is an important quantitative notion of correlation decay for Gibbs
distributions arising in statistical physics, probability theory, and theoretical computer …

We study the mixing time of the Glauber dynamics for general spin systems on the regular
tree, including the Ising model, the hard‐core model (independent sets), and the …

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 …

We analyze Markov chains for generating a random k‐coloring of a random graph Gn, d/n.
When the average degree d is constant, a random graph has maximum degree Θ (log n/log …

Monte Carlo algorithms often depend on Markov chains to sample from very large data sets.
A key ingredient in the design of an efficient Markov chain is determining rigorous bounds …

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 …

We present an improved “cooling schedule” for simulated annealing algorithms for
combinatorial counting problems. Under our new schedule the rate of cooling accelerates as …

We give an online algorithm that with high probability computes a (e/e− 1+ o (1)) Δ edge
coloring on a graph G with maximum degree Δ= ω (log n) under online edge arrivals against …