Long-range contact process and percolation on a random lattice

Pablo A. Gomes and Bernardo N.B. de Lima

Stochastic Processes and their Applications, 2022, vol. 153, issue C, 21-38

Abstract: We study the phase transition phenomena for long-range oriented percolation and contact process. We study a contact process in which the range of each vertex are independent, updated dynamically and given by some distribution N. We also study an analogous oriented percolation model on the hyper-cubic lattice, here there is a special direction where long-range oriented bonds are allowed; the range of all vertices are given by an i.i.d. sequence of random variables with common distribution N. For both models, we prove some results about the existence of a phase transition in terms of the distribution N.

Keywords: Contact process; Long-range percolation; Anisotropic percolation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.07.005

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