Kapfer Krauth 2013

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Revision as of 23:31, 22 January 2013

S. C. Kapfer and W. Krauth 'Sampling from a polytope and hard-disk Monte Carlo' arXiv 1301.4901

Abstract The hard-disk problem, the statics and the dynamics of equal two-dimensional hard spheres in a periodic box, has had a profound inflence on statistical and computational physics. Markov-chain Monte Carlo and molecular dynamics were fi�rst discussed for this model. Here we reformulate hard-disk Monte Carlo algorithms in terms of another classic problem, namely the sampling from a polytope. Local Markov-chain Monte Carlo, as proposed by Metropolis et al. in 1953, appears as a sequence of random walks in high-dimensional polytopes, while the moves of the more powerful event-chain algorithm correspond to molecular dynamics evolution. We determine the convergence properties of Monte Carlo methods in a special invariant polytope associated with hard-disk con�gurations, and the implications for convergence of hard-disk sampling. Finally, we discuss parallelization strategies for event-chain Monte Carlo and present results for a multicore implementation.

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