The survival of branching annihilating random walk

Maury Bramson, Lawrence Gray

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

Branching annihilating random walk is an interacting particle system on ℤ. As time evolves, particles execute random walks and branch, and disappear when they meet other particles. It is shown here that starting from a finite number of particles, the system will survive with positive probability if the random walk rate is low enough relative to the branching rate, but will die out with probability one if the random walk rate is high. Since the branching annihilating random walk is non-attractive, standard techniques usually employed for interacting particle systems are not applicable. Instead, a modification of a contour argument by Gray and Griffeath is used.

Original languageEnglish (US)
Pages (from-to)447-460
Number of pages14
JournalZeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete
Volume68
Issue number4
DOIs
StatePublished - Dec 1 1985

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