Exponential decay of connection probabilities for subcritical Voronoi percolation in $$mathbb {R}^d$$Rd
Exponential decay of connection probabilities for subcritical Voronoi percolation in $$mathbb {R}^d$$Rd
复制标题
$$mathbb {R}^d$$Rd 中亚临界 Voronoi 渗透的连接概率的指数衰减
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
V. Tassion
中科院分区：
文献类型：
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作者：
H. Duminil;Aran Raoufi;V. Tassion
We prove that for Voronoi percolation on $$mathbb {R}^d$$Rd$$(dge 2)$$(d≥2), there exists $$p_c=p_c(d)in (0,1)$$pc=pc(d)∈(0,1) such thatfor $$p0$$cp>0 such that $$mathbb {P}_p[0 ext { connected to distance }n]le exp (-c_pn)$$Pp[0connected to distancen]≤exp(-cpn),there exists $$c>0$$c>0 such that for $$p>p_c, mathbb {P}_p[0 ext { connected to infinity}]ge c(p-p_c)$$p>pc,Pp[0connected to infinity]≥c(p-pc). For dimension 2, this result offers a new way of showing that $$p_c(2)=1/2$$pc(2)=1/2. This paper belongs to a series of papers using the theory of algorithms to prove sharpness of the phase transition; see [10, 11].
淬火 Voronoi 渗透
影响因子：
1.7
作者：
Ahlberg D
通讯作者：
Ahlberg D