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 …

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 …

The purpose of this dissertation is to introduce a version of Stein's method of exchangeable
pairs to solve problems in measure concentration. We specifically target systems of …

The reconstruction problem on the tree plays a key role in several important computational
problems. Deep conjectures in statistical physics link the reconstruction problem to …

In this article we propose new methods for computing the asymptotic value for the logarithm
of the partition function (free energy) for certain statistical physics models on certain type of …

We study a simple Markov chain, known as the Glauber dynamics, for randomly sampling
(proper) k-colorings of an input graph G on n vertices with maximum degree/spl Delta/and …

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 a new lower bound on the spectral gap of the Glauber dynamics for the Gibbs
distribution of a spectrally independent $ q $-spin system on a graph $ G=(V, E) $ with …

We give a polynomial time deterministic approximation algorithm (an FPTAS) for counting
the number of q-colorings of a graph of maximum degree Delta, provided only that q≥ …

We give the first deterministic fully polynomial-time approximation scheme (FPTAS) for
computing the partition function of a two-state spin system on an arbitrary graph, when the …