Approximating stationary distributions of fast mixing Glauber dynamics, with applications to exponential random graphs

TL;DR

This paper introduces a method to bound the Wasserstein distance between distributions of Bernoulli sequences using Glauber dynamics mixing properties, with applications to Ising models and exponential random graphs in high-temperature regimes.

Contribution

It provides a new general bound on Wasserstein distance leveraging Glauber dynamics mixing times, applicable to complex probabilistic models.

Findings

Explicit error bounds for expectations in Ising models.

Effective approximation techniques for exponential random graphs.

Demonstrates high-temperature regime applicability.

Abstract

We provide a general bound on the Wasserstein distance between two arbitrary distributions of sequences of Bernoulli random variables. The bound is in terms of a mixing quantity for the Glauber dynamics of one of the sequences, and a simple expectation of the other. The result is applied to estimate, with explicit error, expectations of functions of random vectors for some Ising models and exponential random graphs in "high temperature" regimes.