A multitype contact process with frozen sites

A spatial model of allelopathy

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1109-1119
Number of pages11
JournalJournal of Applied Probability
Volume42
Issue number4
DOIs
StatePublished - Dec 2005
Externally publishedYes

Fingerprint

Multitype
Contact Process
Spatial Model
Die
Interacting Particle Systems
Duality
Phase Transition
Spatial model
Phase transition

Keywords

  • Allelopathy
  • Competition model
  • Duality
  • Interacting particle system
  • Multitype contact process
  • Phase transition

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

A multitype contact process with frozen sites : A spatial model of allelopathy. / Lanchier, Nicolas.

In: Journal of Applied Probability, Vol. 42, No. 4, 12.2005, p. 1109-1119.

Research output: Contribution to journalArticle

@article{eec5bca148fa4d7b9979e61110b4de2a,
title = "A multitype contact process with frozen sites: A spatial model of allelopathy",
abstract = "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 = "Allelopathy, Competition model, Duality, Interacting particle system, Multitype contact process, Phase transition",
author = "Nicolas Lanchier",
year = "2005",
month = "12",
doi = "10.1239/jap/1134587820",
language = "English (US)",
volume = "42",
pages = "1109--1119",
journal = "Journal of Applied Probability",
issn = "0021-9002",
publisher = "University of Sheffield",
number = "4",

}

TY - JOUR

T1 - A multitype contact process with frozen sites

T2 - A spatial model of allelopathy

AU - Lanchier, Nicolas

PY - 2005/12

Y1 - 2005/12

N2 - 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.

AB - 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.

KW - Allelopathy

KW - Competition model

KW - Duality

KW - Interacting particle system

KW - Multitype contact process

KW - Phase transition

UR - http://www.scopus.com/inward/record.url?scp=33645341192&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645341192&partnerID=8YFLogxK

U2 - 10.1239/jap/1134587820

DO - 10.1239/jap/1134587820

M3 - Article

VL - 42

SP - 1109

EP - 1119

JO - Journal of Applied Probability

JF - Journal of Applied Probability

SN - 0021-9002

IS - 4

ER -