Lei Krauth 2018
From Werner KRAUTH
Revision as of 22:38, 15 October 2018 Werner (Talk | contribs) ← Previous diff |
Current revision Werner (Talk | contribs) |
||
Line 1: | Line 1: | ||
- | '''Z. Lei, W. Krauth''' '''''Mixing and perfect sampling in one-dimensional particle systems''''' '''arXiv:1806.06786 to appear in EPL''' | + | '''Z. Lei, W. Krauth''' '''''Mixing and perfect sampling in one-dimensional particle systems''''' '''EPL 124, 20003(2018)''' |
=Paper= | =Paper= | ||
Line 5: | Line 5: | ||
'''Abstract''' | '''Abstract''' | ||
We study the approach to equilibrium of the event-chain Monte Carlo (ECMC) algorithm for the one-dimensional hard-sphere model. Using the connection to the coupon-collector problem, we prove that a specific version of this local irreversible Markov chain realizes perfect sampling in O(N^2 log N) events, whereas the reversible local Metropolis algorithm requires O(N^3 log N) time steps for mixing. This confirms a special case of an earlier conjecture about O(N^2 log N) scaling of mixing times of ECMC and of the forward Metropolis algorithm, its discretized variant. We furthermore prove that sequential ECMC (with swaps) realizes perfect sampling in O(N^2) events. Numerical simulations indicate a cross-over towards O(N^2 log N) mixing for the sequential forward swap Metropolis algorithm, that we introduce here. We point out open mathematical questions and possible applications of our findings to higher-dimensional statistical-physics models. | We study the approach to equilibrium of the event-chain Monte Carlo (ECMC) algorithm for the one-dimensional hard-sphere model. Using the connection to the coupon-collector problem, we prove that a specific version of this local irreversible Markov chain realizes perfect sampling in O(N^2 log N) events, whereas the reversible local Metropolis algorithm requires O(N^3 log N) time steps for mixing. This confirms a special case of an earlier conjecture about O(N^2 log N) scaling of mixing times of ECMC and of the forward Metropolis algorithm, its discretized variant. We furthermore prove that sequential ECMC (with swaps) realizes perfect sampling in O(N^2) events. Numerical simulations indicate a cross-over towards O(N^2 log N) mixing for the sequential forward swap Metropolis algorithm, that we introduce here. We point out open mathematical questions and possible applications of our findings to higher-dimensional statistical-physics models. | ||
+ | |||
+ | |||
[http://arxiv.org/pdf/1806.06786 Electronic version (from arXiv)] | [http://arxiv.org/pdf/1806.06786 Electronic version (from arXiv)] | ||
+ | |||
+ | |||
+ | [https://doi.org/10.1209/0295-5075/124/20003 Published version (subscription needed)] |
Current revision
Z. Lei, W. Krauth Mixing and perfect sampling in one-dimensional particle systems EPL 124, 20003(2018)
Paper
Abstract We study the approach to equilibrium of the event-chain Monte Carlo (ECMC) algorithm for the one-dimensional hard-sphere model. Using the connection to the coupon-collector problem, we prove that a specific version of this local irreversible Markov chain realizes perfect sampling in O(N^2 log N) events, whereas the reversible local Metropolis algorithm requires O(N^3 log N) time steps for mixing. This confirms a special case of an earlier conjecture about O(N^2 log N) scaling of mixing times of ECMC and of the forward Metropolis algorithm, its discretized variant. We furthermore prove that sequential ECMC (with swaps) realizes perfect sampling in O(N^2) events. Numerical simulations indicate a cross-over towards O(N^2 log N) mixing for the sequential forward swap Metropolis algorithm, that we introduce here. We point out open mathematical questions and possible applications of our findings to higher-dimensional statistical-physics models.