论文标题
在高尺寸的凸粒的布尔模型中渗透
Percolation in the Boolean model with convex grains in high dimension
论文作者
论文摘要
我们研究了凸粒高维的布尔模型中的渗透。对于每个维度D，一个人可以用非空内部固定紧凑，凸和对称集k $ \ subset $ r d。在第一个设置中，布尔模型是K的翻译团聚。在第二个环境中，布尔模型是k或$ρ$ k的翻译团聚，用于进一步的参数$ρ$ $ \ in $（1，2）。我们给出了两个设置中渗透概率和渗透阈值的渐近行为。
We investigate percolation in the Boolean model with convex grains in high dimension. For each dimension d, one fixes a compact, convex and symmetric set K $\subset$ R d with non empty interior. In a first setting, the Boolean model is a reunion of translates of K. In a second setting, the Boolean model is a reunion of translates of K or $ρ$K for a further parameter $ρ$ $\in$ (1, 2). We give the asymptotic behavior of the percolation probability and of the percolation threshold in the two settings.
