Open Access
2015 Contact process on one-dimensional long range percolation
Van Hao Can
Author Affiliations +
Electron. Commun. Probab. 20: 1-11 (2015). DOI: 10.1214/ECP.v20-4461


<span style="color: #000000;">Recently, by introducing the notion of cumulatively merged partition, M<span style="color: #800000;">énard<span style="color: #000000;"> and Singh provide <span style="color: #000000;">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.


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Van Hao Can. "Contact process on one-dimensional long range percolation." Electron. Commun. Probab. 20 1 - 11, 2015.


Accepted: 17 December 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1334.82044
MathSciNet: MR3438738
Digital Object Identifier: 10.1214/ECP.v20-4461

Primary: 82C22
Secondary: 05C80 , 60K35

Keywords: contact process , Cumulative merging , Long range percolation

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