通过运输对具有约束的格点路径进行随机采样
Random sampling of lattice paths with constraints, via transportation
摘要：
本文讨论了带约束的一维格点路径的随机抽样的蒙特卡罗马尔可夫链（MCMC）方法。我们发现，灵感来自最优输运的方法，使我们能够有效地绑定相关的马尔可夫链的混合时间。该算法鲁棒性强，易于实现，并在$n^{3+\eps}$步骤中采样长度为$n$的“几乎”均匀路径。该界利用了马尔可夫链的某种收缩性质，并且还用于推导Propp-Wilson CFTP算法的运行时间的界。
英文摘要：
We discuss a Monte Carlo Markov Chain (MCMC) procedure for the random sampling of some one-dimensional lattice paths with constraints, for various constraints. We show that an approach inspired by optimal transport allows us to bound efficiently the mixing time of the associated Markov chain. The algorithm is robust and easy to implement, and samples an "almost" uniform path of length $n$ in $n^{3+\eps}$ steps. This bound makes use of a certain contraction property of the Markov chain, and is also used to derive a bound for the running time of Propp-Wilson's CFTP algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
