超越可绕性：六顶点模型的FPRAS
Beyond Windability: An FPRAS for The Six-Vertex Model
摘要：
六顶点模型是统计物理中的一个重要模型，与计数问题有着密切的联系。对于六顶点模型[30，10]，已经有一些完全多项式随机逼近方案（FPRAS），它们都要求约束函数是可缠绕的。本文用马尔可夫链蒙特卡罗方法（MCMC）给出了约束函数可展开的六顶点模型的FPRAS。与文献[10]不同的是，我们利用Glauber动力学设计了依赖于底层图的电路分解的马尔可夫链。此外，我们证明了马尔可夫链的快速混合是通过耦合来实现的，而不是文献[10]中的标准路。
英文摘要：
The six-vertex model is an important model in statistical physics and has deep connections with counting problems. There have been some fully polynomial randomized approximation schemes (FPRAS) for the six-vertex model [30, 10], which all require that the constraint functions are windable. In the present paper, we give an FPRAS for the six-vertex model with an unwindable constraint function by Markov Chain Monte Carlo method (MCMC). Different from [10], we use the Glauber dynamics to design the Markov Chain depending on a circuit decomposition of the underlying graph. Moreover, we prove the rapid mixing of the Markov Chain by coupling, instead of canonical paths in [10].
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。
