论文标题
在化学距离和局部唯一性方面，具有足够的超临界装饰随机中间
On Chemical Distance and Local Uniqueness of a Sufficiently Supercritical Finitary Random Interlacement
论文作者
论文摘要
在本文中，我们研究了一个足够超临界的粉饰随机讲述$ \ MATHCAL {fi}^{u，t} $在$ \ mathbb {z}^d，\ d，\ d d $ 3 $中。我们证明，$γ$中的化学距离具有与欧几里得距离$ \ Mathbb {z}^d $相同的指数高概率。这也意味着与Bernoulli渗透和随机讲述平行的形状定理。我们还证明了$ \ Mathcal {fi}^{u，t} $的局部唯一性，它说$ \ Mathcal {fi}^{u，t} $中的任何两个大簇相互接近“彼此之间”将在其之间相同的距离内连接到相同的距离。
In this paper, we study geometric properties of the unique infinite cluster $Γ$ in a sufficiently supercritical Finitary Random Interlacements $\mathcal{FI}^{u,T}$ in $\mathbb{Z}^d, \ d\ge 3$. We prove that the chemical distance in $Γ$ is, with stretched exponentially high probability, of the same order as the Euclidean distance in $\mathbb{Z}^d$. This also implies a shape theorem parallel to those for Bernoulli percolation and random interlacements. We also prove local uniqueness of $\mathcal{FI}^{u,T}$, which says any two large clusters in $\mathcal{FI}^{u,T}$ "close to each other" will with stretched exponentially high probability be connected to each other within the same order of the distance between them.
