The infinite rate symbiotic branching model: from discrete to continuous space
نویسندگان
چکیده
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. 2010 Mathematics Subject Classification: Primary 60K35, Secondary 60J80, 60H15.
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