Phase transitions and duality properties of a successional model

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1 Scopus citations

Abstract

The first purpose of this article is to study the phase transitions of a new interacting particle system. We consider two types of particle, each of which gives birth to particles of the same type as the parent. Particles of the second type can die, whereas those of the first type mutate into the second type. We prove that the three possible outcomes of the process, that is, extinction, survival of the type-2s, or coexistence, may each occur, depending on the selected parameters. Our second, and main, objective, however, is to investigate the duality properties of the process; the corresponding dual process exhibits a structure somewhat different to that of well-known particle systems.

Original languageEnglish (US)
Pages (from-to)265-278
Number of pages14
JournalAdvances in Applied Probability
Volume37
Issue number1
DOIs
StatePublished - Mar 1 2005

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics

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