Kapfer Krauth 2013
From Werner KRAUTH
| Revision as of 23:31, 22 January 2013 Werner (Talk | contribs) ← Previous diff |
Revision as of 23:31, 22 January 2013 Werner (Talk | contribs) Next diff → |
||
| Line 4: | Line 4: | ||
| 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. | ||
| - | Markov-chain Monte Carlo and molecular dynamics were fi�rst 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 | ||
| sampling from a polytope. Local Markov-chain Monte Carlo, as proposed by Metropolis et al. in | sampling from a polytope. Local Markov-chain Monte Carlo, as proposed by Metropolis et al. in | ||
| Line 10: | Line 10: | ||
| of the more powerful event-chain algorithm correspond to molecular dynamics evolution. We | 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 | 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 | + | 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 | sampling. Finally, we discuss parallelization strategies for event-chain Monte Carlo and present | ||
| results for a multicore implementation. | results for a multicore implementation. | ||
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 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.
