Comparing exponential and Erdős–Rényi random graphs, and a general bound on the distance between Bernoulli random vectors

Comparing exponential and Erdős–Rényi random graphs, and a general bound on the distance between Bernoulli random vectors

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Nathan Ross, University of Melbourne
Fine Hall 601

We present a general bound on the Wasserstein distance between two arbitrary distributions of sequences of Bernoulli random variables. The bound is in terms of 1) a mixing quantity for the Glauber dynamics of one of the sequences, and 2) 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. Joint work with Gesine Reinert.