Poisson percolation on the oriented square lattice

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 sh...

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Bibliographic Details
Published in:Stochastic processes and their applications 2020-02, Vol.130 (2), p.488-502
Main Authors: Cristali, Irina, Junge, Matthew, Durrett, Rick
Format: Article
Language:English
Subjects:
Block construction
Oriented
Percolation
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Summary: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.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2019.01.005