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

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