We say a probability distribution μ is spectrally independent if an associated pairwise
influence matrix has a bounded largest eigenvalue for the distribution and all of its …

Consider the problem of approximately counting weighted independent sets of a graph G
with activity λ, ie, where the weight of an independent set I is λ| I|. We present a novel …

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 …

We prove an optimal lower bound on a spectral gap of the Glauber dynamics for
antiferromagnetic two-spin systems with vertices in the tree uniqueness regime. This …

We prove an optimal Ω(n^-1) lower bound for modified \log-Sobolev (MLS) constant of the
Glauber dynamics for anti-ferromagnetic two-spin systems with n vertices in the tree …

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 introduce a framework for obtaining tight mixing times for Markov chains based on what
we call restricted modified log-Sobolev inequalities. Modified log-Sobolev inequalities …

We establish tight results for rapid mixing of Gibbs samplers for the Ferromagnetic Ising
model on general graphs. We show that if (d-1)\tanhβ<1, then there exists a constant C such …

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 …

We give a near-linear time sampler for the Gibbs distribution of the ferromagnetic Ising
models with edge activities β> 1 and external fields λ< 1 (or symmetrically, λ> 1) on general …