Rapid Mixing of Several Markov Chains for a Hard-Core Model

The mixing properties of several Markov chains to sample from configurations of a hard-core model have been examined. The model is familiar in the statistical physics of the liquid state and consists of a set of n nonoverlapping particle balls of radius r∗ in a d-dimensional hypercube. Starting from an initial configuration, standard Markov chain monte carlo methods may be employed to generate a configuration according to a probability distribution of interest by choosing a trial state and accepting or rejecting the trial state as the next configuration of the Markov chain according to the Metropolis filter. Procedures to generate a trial state include moving a single particle globally within the hypercube, moving a single particle locally, and moving multiple particles at once. We prove that (i) in a d-dimensional system a single-particle globalmove Markov chain is rapidly mixing as long as the density is sufficiently low, (ii) in a one-dimensional system a single-particle loca...

• Type: Conference
• Year: 2003
• Where: ISAAC
• Authors: Ravi Kannan, Michael W. Mahoney, Ravi Montenegro
• Keywords: ISAAC 2003, Local-move Markov Chains, Markov Chains, Trial State