Brownian net with killing

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

Stochastic Processes and their Applications, 2015, vol. 125, issue 3, 1148-1194

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.

Keywords: Brownian motion; Brownian web; Voter model perturbations (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spa.2014.09.018

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