Long-range contact process and percolation on a random lattice

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 $N$.

References in corpus (4)

• On the scaling of the chemical distance in long-range percolation models
• Mean-field driven first-order phase transitions in systems with long-range interactions
• Contact processes with long-range interactions
• Results on the contact process with dynamic edges or under renewals