Arm exponents in high dimensional percolation
Arm exponents in high dimensional percolation
复制标题
高维渗透中的 Arm 指数
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Asaf Nachmias
中科院分区：
文献类型：
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作者：
G. Kozma;Asaf Nachmias
我们研究了在高维临界渗流中，即当维数d足够大或d>6且晶格充分展开时，原点连接到半径为r的球（臂事件）的概率。我们证明这个概率像1/r^2那样衰减。此外，我们还证明了从原点附近发出距离为r的k个不相交臂的概率为1/r^2k。
We study the probability that the origin is connected to the sphere of radius r (an arm event) in critical percolation in high dimensions, namely when the dimension d is large enough or when d>6 and the lattice is sufficiently spread out. We prove that this probability decays like 1/r^2. Furthermore, we show that the probability of having k disjoint arms to distance r emanating from the vicinity of the origin is 1/r^2k.