The Annals of Applied Probability

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

Gesine Reinert and Nathan Ross

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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.

Article information

Ann. Appl. Probab., Volume 29, Number 5 (2019), 3201-3229.

Received: December 2017
Revised: January 2019
First available in Project Euclid: 18 October 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 60B10: Convergence of probability measures
Secondary: 05C80: Random graphs [See also 60B20]

Glauber dynamics exponential random graphs Stein’s method


Reinert, Gesine; Ross, Nathan. Approximating stationary distributions of fast mixing Glauber dynamics, with applications to exponential random graphs. Ann. Appl. Probab. 29 (2019), no. 5, 3201--3229. doi:10.1214/19-AAP1478.

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