Brownian net with killing

C. M. Newman, K. Ravishankar, E. Schertzer

Research output: Contribution to journalArticle

Abstract

Motivated by its relevance for the study of perturbations of one-dimensional voter models, including stochastic Potts models at low temperature, we consider diffusively rescaled coalescing random walks with branching and killing. Our main result is convergence to a new continuum process, in which the random space-time paths of the Sun-Swart Brownian net are terminated at a Poisson cloud of killing points. We also prove existence of a percolation transition as the killing rate varies. Key issues for convergence are the relations of the discrete model killing points and their intensity measure to the continuum counterparts: these convergence issues make the addition of killing considerably more difficult for the Brownian net than for the Brownian web.

Original languageEnglish (US)
Pages (from-to)1148-1194
Number of pages47
JournalStochastic Processes and their Applications
Volume125
Issue number3
DOIs
StatePublished - 2015

Keywords

  • Brownian motion
  • Brownian web
  • Voter model perturbations

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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