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Preprint 08-2015

The infinite rate symbiotic branching model: from discrete to continuous space

Source file is available as :   Portable Document Format (PDF)

Author(s) : Matthias Hammer , Marcel Ortgiese

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 08-2015

MSC 2000

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60J80 Branching processes
60H15 Stochastic partial differential equations

Abstract :
The symbiotic branching model describes a spatial population consisting of two types that are allowed to migrate in space and branch locally only if both types are present. We continue our investigation of the large scale behaviour of the system started in [BHO15], where we showed that the continuum system converges after diffusive rescaling. Inspired by a scaling property of the continuum model, a series of earlier works initiated by Klenke and Mytnik [KM12a, KM12b] studied the model on a discrete space, but with infinite branching rate. In this paper, we bridge the gap between the two models by showing that by diffusively rescaling the discrete space infinite rate model we obtain our continuum model.

Keywords : Symbiotic branching model, mutually catalytic branching, stepping stone model, rescaled interface, moment duality, Meyer-Zheng topology

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