We consider two related tasks:(a) estimating a parameterisation of a given Gibbs state and
expectation values of Lipschitz observables on this state;(b) learning the expectation values …

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 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 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 …

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 present a simple algorithm that perfectly samples configurations from the unique Gibbs
measure of a spin system on a potentially infinite graph G. The sampling algorithm assumes …

The independence polynomial of a graph is the generating polynomial of all its independent
sets. Formally, given a graph G, its independence polynomial ZG (λ) is given by Σ I λ| I …

In this paper we show that absence of complex zeros of the partition function of the hard-
core model on any family of bounded degree graphs that is closed under taking induced …