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• W2808060068 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." @default.
• W2808060068 created "2018-06-21" @default.
• W2808060068 creator A5070815065 @default.
• W2808060068 creator A5080439775 @default.
• W2808060068 date "2018-11-19" @default.
• W2808060068 modified "2023-10-15" @default.
• W2808060068 title "Mixing and perfect sampling in one-dimensional particle systems" @default.
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• W2808060068 doi "https://doi.org/10.1209/0295-5075/124/20003" @default.
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