Monte Carlo methods use random sampling to estimate numerical quantities which are hard
to compute deterministically. One important example is the use in statistical physics of …

We prove an optimal mixing time bound for the single-site update Markov chain known as
the Glauber dynamics or Gibbs sampling in a variety of settings. Our work presents an …

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 …

For general spin systems, we prove that a contractive coupling for an arbitrary local Markov
chain implies optimal bounds on the mixing time and the modified log-Sobolev constant for a …

The hardcore model is a model of lattice gas systems which has received much attention in
statistical physics, probability theory and theoretical computer science. It is the probability …

For general antiferromagnetic 2-spin systems, including the hardcore model on weighted
independent sets and the antiferromagnetic Ising model, there is an for the partition function …

We introduce a notion called entropic independence that is an entropic analog of spectral
notions of high-dimensional expansion. Informally, entropic independence of a background …

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 …

Markov chain Monte Carlo algorithms have important applications in counting problems and
in machine learning problems, settings that involve estimating quantities that are difficult to …