Long-range contact process and percolation on a random lattice

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

doi:10.1016/j.spa.2022.07.005

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arXiv · 2108.13531

Long-range contact process and percolation on a random lattice

Pablo A. Gomes·Bernardo N. B. de Lima

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Abstract

We study the phase transition phenomena for long-range oriented percolation and contact process. We studied 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 $N$.

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Pablo A. Gomes, Bernardo N. B. de Lima. 2021-08-30. Long-range contact process and percolation on a random lattice. https://doi.org/10.1016/j.spa.2022.07.005

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