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 language | English (US) |
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Pages (from-to) | 1148-1194 |
Number of pages | 47 |
Journal | Stochastic Processes and their Applications |
Volume | 125 |
Issue number | 3 |
DOIs | |
State | Published - 2015 |
Keywords
- Brownian motion
- Brownian web
- Voter model perturbations
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics