Mixing Time of Glauber Dynamics With Parallel Updates and Heterogeneous Fugacities

Details Mixing Time of Glauber Dynamics With Parallel Updates and Heterogeneous Fugacities Mixing Time of Glauber Dynamics With Parallel Updates and Heterogeneous Fugacities

2010-04-02

arxiv.org/abs/1004.0397v1

Mathematics

Probability

15 pages

Scientific paper

Glauber dynamics is a powerful tool to generate randomized, approximate solutions to combinatorially difficult problems. Applications include Markov Chain Monte Carlo (MCMC) simulation and distributed scheduling for wireless networks. In this paper, we derive bounds on the mixing time of a generalization of Glauber dynamics where multiple vertices are allowed to update their states in parallel and the fugacity of each vertex can be different. The results can be used to obtain various conditions on the system parameters such as fugacities, vertex degrees and update probabilities, under which the mixing time grows polynomially in the number of vertices.

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