低温Potts模型中通过流场上的马尔可夫链的采样
Sampling from the low temperature Potts model through a Markov chain on flows
摘要：
本文研究了低温下Potts模型的采样和分拆函数的计算问题。而不是直接与自旋配置工作，我们认为采样流的等效问题。我们表明，使用路径耦合，一个简单的和自然的马尔可夫链上的流集是迅速混合。结果发现在足够低的温度下Potts模型的一个$δ$ -近似抽样算法，对于有$m$边的图$G$，其运行时间以$O(m^2\log(mδ^{-1}))$为界.
英文摘要：
In this paper we consider the algorithmic problem of sampling from the Potts model and computing its partition function at low temperatures. Instead of directly working with spin configurations, we consider the equivalent problem of sampling flows. We show, using path coupling, that a simple and natural Markov chain on the set of flows is rapidly mixing. As a result we find a $δ$-approximate sampling algorithm for the Potts model at low enough temperatures, whose running time is bounded by $O(m^2\log(mδ^{-1}))$ for graphs $G$ with $m$ edges.
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。
