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Rescaled contact processes converge to super-Brownian motion in two or more dimensions
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  • Published: June 1999

Rescaled contact processes converge to super-Brownian motion in two or more dimensions

  • Richard Durrett1 &
  • Edwin A. Perkins2 

Probability Theory and Related Fields volume 114, pages 309–399 (1999)Cite this article

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  • 42 Citations

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Abstract.

We show that in dimensions two or more a sequence of long range contact processes suitably rescaled in space and time converges to a super-Brownian motion with drift. As a consequence of this result we can improve the results of Bramson, Durrett, and Swindle (1989) by replacing their order of magnitude estimates of how close the critical value is to 1 with sharp asymptotics.

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Authors and Affiliations

  1. Department of Mathematics and ORIE, 278 Rhodes Hall, Cornell University, Ithaca, NY 14853, USA (e-mail: rtd1@cornell.edu), , , , , , US

    Richard Durrett

  2. Department of Mathematics, 1984 Mathematics Rd., University of British Columbia, Vancouver, B.C. V6T 1Z2, Canada (e-mail: perkins@math.ubc.ca), , , , , , CA

    Edwin A. Perkins

Authors
  1. Richard Durrett
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  2. Edwin A. Perkins
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Received: 2 February 1998 / Revised version: 28 August 1998

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Durrett, R., Perkins, E. Rescaled contact processes converge to super-Brownian motion in two or more dimensions. Probab Theory Relat Fields 114, 309–399 (1999). https://doi.org/10.1007/s004400050228

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  • Issue Date: June 1999

  • DOI: https://doi.org/10.1007/s004400050228

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  • Mathematics Subject Classification (1991): Primary 60K35, 60G57; Secondary: 60F05, 60J80
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