Poisson percolation on the oriented square lattice


Journal Article

© 2019 Elsevier B.V. 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.

Full Text

Duke Authors

Cited Authors

  • Cristali, I; Junge, M; Durrett, R

Published Date

  • February 1, 2020

Published In

Volume / Issue

  • 130 / 2

Start / End Page

  • 488 - 502

International Standard Serial Number (ISSN)

  • 0304-4149

Digital Object Identifier (DOI)

  • 10.1016/j.spa.2019.01.005

Citation Source

  • Scopus