# Lei Krauth 2018

### From Werner KRAUTH

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- | '''Z. Lei, W. Krauth''' '''''Mixing and perfect sampling in one-dimensional particle systems''''' '''arXiv:1806.06786''' | + | '''Z. Lei, W. Krauth''' '''''Mixing and perfect sampling in one-dimensional particle systems''''' '''arXiv:1806.06786 to appear in EPL''' |

=Paper= | =Paper= |

## Revision as of 22:38, 15 October 2018

**Z. Lei, W. Krauth** **Mixing and perfect sampling in one-dimensional particle systems****arXiv:1806.06786 to appear in EPL**

# 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.