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 …

Graphs are naturally associated with matrices, as matrices provide a simple way of
representing graphs in computer memory. The basic one of these is the adjacency matrix …

The motivation of this work is to extend the techniques of higher order random walks on
simplicial complexes to analyze mixing times of Markov chains for combinatorial problems …

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 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 that Ising models on the hypercube with general quadratic interactions satisfy a
Poincaré inequality with respect to the natural Dirichlet form corresponding to Glauber …

Graph-based machine learning is experiencing explosive growth, driven by impressive
recent developments and wide applicability. Typical approaches for graph representation …

Given samples from an unknown multivariate distribution p, is it possible to distinguish
whether p is the product of its marginals versus p being far from every product distribution …

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 …