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On the Growth of the One-Dimensional Reverse Immunization Contact Processes

Part of: Special processes Time-dependent statistical mechanics (dynamic and nonequilibrium)

Published online by Cambridge University Press:  14 July 2016

A. Tzioufas
A. Tzioufas*
Affiliation:
Heriot-Watt University
*
∗ Postal address: Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh EH14 4AS, UK. Email address: [email protected]
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Abstract

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We are concerned with the variation of the supercritical nearest-neighbours contact process such that first infection occurs at a lower rate; it is known that the process survives with positive probability. Regarding the rightmost infected of the process started from one site infected and conditioned to survive, we specify a sequence of space-time points at which its behaviour regenerates and, thus, obtain the corresponding strong law and central limit theorem. We also extend complete convergence in this case.

Keywords

Contact processKuczek-type argument

MSC classification

Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory 82C22: Interacting particle systems
Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 3 , September 2011 , pp. 611 - 623
Copyright
Copyright © Applied Probability Trust 2011 

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