Ising模型的匹配化约
Reducing the Ising model to matchings
摘要：
典型路径是一个最强大的工具，可用于显示一个马尔可夫链是快速混合，从而使近似抽样复杂的高维分布。规范路径方法的两个成功案例是在图中绘制匹配的链，以及称为子图世界的伊辛模型版本的链。在本文中，它表明，子图的世界绘制可以通过采取绘制从匹配的图，是线性的原始图的大小。这提供了一个部分的答案，为什么典型的路径工程，以及为伊辛模型的算法提供了一个新的来源。例如，这种新的减少立即产生一个完全多项式时间的近似计划的伊辛模型的有界度图时，磁化率有界远离0。
英文摘要：
Canonical paths is one of the most powerful tools available to show that a Markov chain is rapidly mixing, thereby enabling approximate sampling from complex high dimensional distributions. Two success stories for the canonical paths method are chains for drawing matchings in a graph, and a chain for a version of the Ising model called the subgraphs world. In this paper, it is shown that a subgraphs world draw can be obtained by taking a draw from matchings on a graph that is linear in the size of the original graph. This provides a partial answer to why canonical paths works so well for both problems, as well as providing a new source of algorithms for the Ising model. For instance, this new reduction immediately yields a fully polynomial time approximation scheme for the Ising model on a bounded degree graph when the magnitization is bounded away from 0.
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。
