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arXiv · 1309.5651

The Brownian Net with Killing

Charles M. Newman·K. Ravishankar·Emmanuel Schertzer
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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 Poisson intensity measure to the continuum counterparts.

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Charles M. Newman, K. Ravishankar, Emmanuel Schertzer. 2013-09-22. The Brownian Net with Killing. https://arxiv.org/abs/1309.5651

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