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A multitype contact process with frozen sites: a spatial model of allelopathy

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Nicolas Lanchier
Nicolas Lanchier*
Affiliation:
Université de Rouen
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Abstract

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In this paper, we introduce a generalization of the two-color multitype contact process intended to mimic a biological process called allelopathy. To be precise, we have two types of particle. Particles of each type give birth to particles of the same type, and die at rate 1. When a particle of type 1 dies, it gives way to a frozen site that blocks particles of type 2 for an exponentially distributed amount of time. Specifically, we investigate in detail the phase transitions and the duality properties of the interacting particle system.

Keywords

Interacting particle systemmultitype contact processcompetition modelallelopathyphase transitionduality

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 4 , December 2005 , pp. 1109 - 1119
Copyright
© Applied Probability Trust 2005 

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