电缆图环路汤与高斯自由场的切换恒等式
A switching identity for cable-graph loop soups and Gaussian free fields
AI总结：
本文提出电缆图环路汤与高斯自由场的切换恒等式，证明两点同簇条件等价于添加随机奇数条独立布朗游程，并由此分析无限图上符号簇的大尺度行为。
摘要：
我们推导出一个“切换恒等式”，该恒等式可针对临界布朗环路汤或电缆图上的高斯自由场（GFF）进行表述：它基本上表明，在簇构型层面以及更一般的占据时间场层面，将电缆图上的两个点条件化为属于同一个布朗环路簇（或等价地属于GFF的同一个符号簇），等价于在这两个点之间向一个原本无条件的构型中添加一个随机奇数条独立的布朗游程。当连接发生时，簇的条件律的这一显式简单描述具有多种直接推论，特别是关于无限图上这些符号簇的大尺度行为。
英文摘要：
We derive a "switching identity" that can be stated for critical Brownian loop-soups or for the Gaussian free field on a cable graph: It basically says that at the level of cluster configurations and at the more general level of the occupation time fields, conditioning two points on the cable-graph to belong to the same cluster of Brownian loops (or equivalently to the same sign-cluster of the GFF) amounts to adding a random odd number of independent Brownian excursions between these points to an otherwise unconditioned configuration. This explicit simple description of the conditional law of the clusters when a connection occurs has various direct consequences, in particular about the large scale behaviour of these sign-clusters on infinite graphs.
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。
