Contact process on one-dimensional long-range percolation
Probability
2016-01-05 v3
Abstract
Recently, by introducing the notion of cumulatively merged partition, M\'enard 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.
Keywords
Cite
@article{arxiv.1506.02372,
title = {Contact process on one-dimensional long-range percolation},
author = {Van Hao Can},
journal= {arXiv preprint arXiv:1506.02372},
year = {2016}
}
Comments
11 p in Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2015