论文标题
平板上的近似和与缺陷平面的不均匀渗透的独特性
Approximation on slabs and uniqueness for inhomogeneous percolation with a plane of defects
论文作者
论文摘要
令$ \ mathbb {l}^{d} =（\ mathbb {z}^{d}，\ mathbb {e}^{d}）$ be $ d $ - d $ - 二级二级超尺寸lattice。我们考虑了$ \ mathbb {l}^{d} $上的不均匀的bernoulli渗透模型，其中$ s $ s $ -dimensional超平面$ \ mathbb {z}^{z}^{s}^{s} {s} {s} \ times \ time times \ {0 \} $ {d-s} $ quartibility quint obity in quartients $ qubity qubitients $ quart in quartient以概率$ p $打开。当$ p \ neq p_ {c}（d）$时，我们证明了无限群集在超批评性方面的独特性，其中$ p_ {c}（c}（d）$表示同质渗透的阈值，并且可以通过$ prient of priend of prient of prime p，q_ {c}（p，p，q_ {c}）。 p_ {c}（d）$。
Let $ \mathbb{L}^{d} = ( \mathbb{Z}^{d},\mathbb{E}^{d} ) $ be the $ d $-dimensional hypercubic lattice. We consider a model of inhomogeneous Bernoulli percolation on $ \mathbb{L}^{d} $ in which every edge inside the $ s $-dimensional hyperplane $ \mathbb{Z}^{s} \times \{ 0 \}^{d-s} $, $ 2 \leq s < d $, is open with probability $ q $ and every other edge is open with probability $ p $. We prove the uniqueness of the infinite cluster in the supercritical regime whenever $ p \neq p_{c}(d) $, where $ p_{c}(d) $ denotes the threshold for homogeneous percolation, and that the critical point $ (p,q_{c}(p)) $ can be approximated on the phase space by the critical points of slabs, for any $ p < p_{c}(d) $.
