From Werner KRAUTH

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	'''Abstract'''		'''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 influence on statistical and computational physics.
	Markov-chain Monte Carlo and molecular dynamics were first discussed for this model. Here we		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		reformulate hard-disk Monte Carlo algorithms in terms of another classic problem, namely the
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	[http://arxiv.org/pdf/1301.4901v1 Electronic version (from arXiv, original version)]		[http://arxiv.org/pdf/1301.4901v1 Electronic version (from arXiv, original version)]
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		+	[[Image:Polytope ballistics plus graph2.jpg|left|100px|border|thumb|Polytopes and constraint graph]]
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Revision as of 11:06, 28 January 2013

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

Contents 1 Paper

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)