带圈汤的符号高斯自由场的耦合反演
Inverting the coupling of the signed Gausssian free field with a loop soup
摘要：
Lupu介绍了一个随机游动环汤和高斯自由场之间的耦合，其中场的符号在每个环簇上都是常数。这种耦合是一个签署版本的同构定理有关的平方GFF占领领域的马尔可夫轨迹。他的构造从一个循环汤开始，通过添加额外的随机性样本，从其中提取GFF。在本文中，我们提供了逆构造：从一个有符号自由场开始，使用与该自由场相关的自交互随机游动，我们构造一个随机游动循环汤。我们的构造依赖于Sabot和Tarrès以前的工作，它从GFF的平方而不是有符号的GFF本身反转耦合。作为结果，我们还推出了一个反演的耦合之间的随机电流和FK-Ising随机集团模型介绍的Lupu和Werner。
英文摘要：
Lupu introduced a coupling between a random walk loop-soup and a Gaussian free field, where the sign of the field is constant on each cluster of loops. This coupling is a signed version of isomorphism theorems relating the square of the GFF to the occupation field of Markovian trajectories. His construction starts with a loop-soup, and by adding additional randomness samples a GFF out of it. In this article we provide the inverse construction: starting from a signed free field and using a self-interacting random walk related to this field, we construct a random walk loop-soup. Our construction relies on the previous work by Sabot and Tarrès, which inverts the coupling from the square of the GFF rather than the signed GFF itself. As a consequence, we also deduce an inversion of the coupling between the random current and the FK-Ising random cluster models introduced by Lupu and Werner.
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。
