Poisson percolation on the oriented square lattice

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Cristali, Irina¹  Junge, Matthew¹  Durrett, Rick¹ 

[1] Duke Univ, Math Dept, Box 90320, Durham, NC 27708 USA

关键词: Percolation;    Block construction;    Oriented;   

DOI  :  10.1016/j.spa.2019.01.005

来源: Elsevier

【 摘 要 】

In Poisson percolation each edge becomes open after an independent exponentially distributed time with rate that decreases in the distance from the origin. As a sequel to our work on the square lattice, we describe the limiting shape of the component containing the origin in the oriented case. We show that the density of occupied sites at height y in the cluster is close to the percolation probability in the corresponding homogeneous percolation process, and we study the fluctuations of the boundary. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

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