Electronic Communications in Probability

Contact process on one-dimensional long range percolation

Van Hao Can

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<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.

Article information

Electron. Commun. Probab., Volume 20 (2015), paper no. 93, 11 pp.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 82C22: Interacting particle systems [See also 60K35]
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 05C80: Random graphs [See also 60B20]

Contact process Cumulative merging Long range percolation

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Can, Van Hao. Contact process on one-dimensional long range percolation. Electron. Commun. Probab. 20 (2015), paper no. 93, 11 pp. doi:10.1214/ECP.v20-4461. https://projecteuclid.org/euclid.ecp/1465321020

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