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Critical first-passage percolation starting on the boundary
Jiang, Jianping1; Yao, Chang-Long2
AbstractWe consider first-passage percolation on the two-dimensional triangular lattice T. Each site v is an element of T is assigned independently a passage time of either 0 or 1 with probability 1/2. Denote by B+(0, n) the upper half-disk with radius n centered at 0, and by c(n)(+) the first-passage time in B+(0, n) from 0 to the half-circular boundary of B+(0, n). We prove lim(n ->infinity) c(n)(+)/log n = root 3/2 pi a.s., lim(n ->infinity) Ec(n)(+)/log n = root 3/2 pi, lim(n ->infinity) Var(c(n)(+)/log n) = 2 root 3/pi - 9/pi(2). These results enable us to prove limit theorems with explicit constants for any first-passage time between boundary points of Jordan domains. In particular, we find the explicit limit theorems for the cylinder point to point and cylinder point to line first-passage times. (C) 2018 Elsevier B.V. All rights reserved.
Funding ProjectSTCSM grant[17YF1413300] ; National Natural Science Foundation of China[11601505] ; National Natural Science Foundation of China[11688101] ; Key Laboratory of Random Complex Structures and Data Science, CAS[2008DP173182]
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000469157100007
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Document Type期刊论文
Corresponding AuthorJiang, Jianping
Affiliation1.NYU Shanghai, NYU ECNU Inst Math Sci, 3663 Zhongshan Rd North, Shanghai 200062, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Jiang, Jianping,Yao, Chang-Long. Critical first-passage percolation starting on the boundary[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS,2019,129(6):2049-2065.
APA Jiang, Jianping,&Yao, Chang-Long.(2019).Critical first-passage percolation starting on the boundary.STOCHASTIC PROCESSES AND THEIR APPLICATIONS,129(6),2049-2065.
MLA Jiang, Jianping,et al."Critical first-passage percolation starting on the boundary".STOCHASTIC PROCESSES AND THEIR APPLICATIONS 129.6(2019):2049-2065.
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