English

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

R2 v1 2026-06-22T09:48:57.450Z