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The birthday problem and Markov chain Monte Carlo

Itai Benjamini·Ben Morris
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Abstract

We study the problem of generating a sample from the stationary distribution of a Markov chain, given a method to simulate the chain. We give an approximation algorithm for the case of a random walk on a regular graph with n vertices that runs in expected time O^*(\sqrt{n} x L^2-mixing time). This is close to the best possible, since \sqrt{n} is a lower bound on the worst-case expected running time of any algorithm.

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Itai Benjamini, Ben Morris. 2007-01-14. The birthday problem and Markov chain Monte Carlo. https://arxiv.org/abs/math/0701390

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