Kapfer Krauth 2013
From Werner KRAUTH
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| '''S. C. Kapfer and W. Krauth''' | '''S. C. Kapfer and W. Krauth''' | ||
| - | '''''Sampling from a polytope and hard-disk Monte Carlo''''' ''' arXiv 1301.4901''' | + | '''''Sampling from a polytope and hard-disk Monte Carlo''''' J. Phys.: Conf. Ser. 454 012031 (2013) |
| =Paper= | =Paper= | ||
Revision as of 22:18, 2 September 2013
S. C. Kapfer and W. Krauth Sampling from a polytope and hard-disk Monte Carlo J. Phys.: Conf. Ser. 454 012031 (2013)
Contents |
Paper
Abstract The hard-disk problem, the statics and the dynamics of equal two-dimensional hard spheres in a periodic box, has had a profound influence on statistical and computational physics. Markov-chain Monte Carlo and molecular dynamics were first 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 configurations, 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.
Electronic version (from arXiv, original version)
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