The birthday problem and Markov chain Monte Carlo
Probability
2007-05-23 v1 Combinatorics
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.
Cite
@article{arxiv.math/0701390,
title = {The birthday problem and Markov chain Monte Carlo},
author = {Itai Benjamini and Ben Morris},
journal= {arXiv preprint arXiv:math/0701390},
year = {2007}
}