Kapfer Krauth 2013
From Werner KRAUTH
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| - | S. C. Kapfer and W. Krauth 'Sampling from a polytope and hard-disk Monte Carlo' arXiv 1301.4901 | + | __FORCETOC__ |
| + | '''S. C. Kapfer and W. Krauth''' | ||
| + | '''''Sampling from a polytope and hard-disk Monte Carlo''''' ''' arXiv 1301.4901''' | ||
| - | ''Abstract'' | + | =Paper= |
| + | |||
| + | '''Abstract''' | ||
| The hard-disk problem, the statics and the dynamics of equal two-dimensional hard | 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. | spheres in a periodic box, has had a profound inflence on statistical and computational physics. | ||
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| sampling. Finally, we discuss parallelization strategies for event-chain Monte Carlo and present | sampling. Finally, we discuss parallelization strategies for event-chain Monte Carlo and present | ||
| results for a multicore implementation. | results for a multicore implementation. | ||
| + | |||
| + | [http://arxiv.org/pdf/1301.4901v1 Electronic version (from arXiv, original version)] | ||
Revision as of 23:35, 22 January 2013
S. C. Kapfer and W. Krauth Sampling from a polytope and hard-disk Monte Carlo arXiv 1301.4901
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 inflence 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.
