论文标题
超越启发性：六胜利模型的FPRA
Beyond Windability: An FPRAS for The Six-Vertex Model
论文作者
论文摘要
六个vertex模型是统计物理学中的重要模型，并且与计数问题具有深厚的联系。六个vertex模型[30，10]有一些完全多项式随机近似方案（FPRA），所有这些模型都要求约束函数有易于函数。在本文中，我们为Markov Chain Monte Carlo方法（MCMC）提供了六个Vertex模型的FPRA。与[10]不同，我们使用Glauber动力学来设计马尔可夫链，具体取决于基础图的电路分解。此外，我们通过耦合证明了马尔可夫链的快速混合，而不是[10]中的规范路径。
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].
