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Brownian net with killing

Author

Listed:
  • Newman, C.M.
  • Ravishankar, K.
  • Schertzer, E.

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.

Suggested Citation

  • Newman, C.M. & Ravishankar, K. & Schertzer, E., 2015. "Brownian net with killing," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 1148-1194.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:3:p:1148-1194
    DOI: 10.1016/j.spa.2014.09.018
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    References listed on IDEAS

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    1. Hisashi Ohtsuki & Christoph Hauert & Erez Lieberman & Martin A. Nowak, 2006. "A simple rule for the evolution of cooperation on graphs and social networks," Nature, Nature, vol. 441(7092), pages 502-505, May.
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