论文标题
Kesten的初期无限簇，用于三维公制的高斯自由场，来自关键级别的渗透以及小人模型，从随机群集几何形状和Swendsen-Wang型算法中。
Kesten's incipient infinite cluster for the three-dimensional, metric-graph Gaussian free field, from critical level-set percolation, and for the Villain model, from random cluster geometries and a Swendsen-Wang type algorithm
论文作者
论文摘要
我们在最近的一项工作中解决了一个空旷的问题，这是由于ding和wirth的最新作品，其第一个版本以$ 2019 $的价格购买，这与级别集合在三个维度上的高斯免费场的度量渗透相关，其中渗透率估算了percolation估算的作者用于研究数字级别的不同高度的polot groy tody lot log log log log log log lot log log log log。在三个维度上，为了构建凯斯滕的初步无限群集，该集群首先是通过两个概率数量的平等，在1986美元的$ 1986 $中为伯努利渗透而引入的，我们利用了由于Basu和sapozhnikov的概率propertive propping propping of 2016 $ n of 2016 $ n of 2016 $，我们使用该简流版本，该版本是$ 2016，该属性是$ 2016，该概率是$ 2016 $，该$ 2016 $ in in $ 2016 $ n in in in y 2016 $ n in in in n $ 2016 $ n.证明IIC存在于无限连接的有界度图上的Bernoulli渗透。为了利用这样的论点在三个维度上证明了公制GFF IIC的存在，我们还解决了由于Dubedat和Falconet的近期$ 2022 $，在最近的一项工作中提出了另一个开放问题，这表达了与小人小人模型的IIC型限制有关的开放问题。
We address one open problem in a recent work due to Ding and Wirth, the first version of which was available in $2019$, relating to level-set percolation on metric-graphs for the Gaussian free field in three dimensions, in which it was shown that a percolation estimate that the authors employ for studying connectivity properties of different heights of the metric graph Gaussian free field is bounded above poly-logarithmically. In three dimensions, in order to construct Kesten's incipient infinite cluster which was first seminally introduced for Bernoulli percolation in two dimensions, in $1986$, through the equality of two probabilistic quantities, we make use of a streamlined version of the $1986$ argument due to Basu and Sapozhnikov, which was first made available in $2016$, that introduces properties of crossing probabilities for demonstrating that the IIC exists for Bernoulli percolation on an infinite connected, bounded degree graph. To make use of such arguments for demonstrating the existence of the metric-graph GFF IIC in three dimensions, we also address another open problem raised in a recent work, from October $2022$, due to Dubedat and Falconet, which expresses an open problem pertaining to the construction of an IIC-type limit for the Villain model.
