Contact process on one-dimensional long-range percolation

Abstract

Recently, by introducing the notion of cumulatively merged partition, Ménard and Singh provide a sufficient condition on graphs ensuring that the critical value of the contact process is positive. In this note, we show that the one-dimensional long range percolation with high exponent satisfies their condition and thus the contact process exhibits a non-trivial phase transition.

11 p in Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2015