## Fastest Mixing Markov Chain on A Graph (2003)

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Venue: | SIAM REVIEW |

Citations: | 88 - 15 self |

### BibTeX

@ARTICLE{Boyd03fastestmixing,

author = {Stephen Boyd and Persi Diaconis and Lin Xiao},

title = {Fastest Mixing Markov Chain on A Graph},

journal = {SIAM REVIEW},

year = {2003},

volume = {46},

pages = {667--689}

}

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### Abstract

We consider a symmetric random walk on a connected graph, where each edge is labeled with the probability of transition between the two adjacent vertices. The associated Markov chain has a uniform equilibrium distribution; the rate of convergence to this distribution, i.e. the mixing rate of the Markov chain, is determined by the second largest (in magnitude) eigenvalue of the transition matrix. In this paper we address the problem of assigning probabilities to the edges of the graph in such a way as to minimize the second largest magnitude eigenvalue, i.e., the problem of finding the fastest mixing Markov chain on the graph. We show that