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The symbiotic branching model describes a spatial population consisting oftwo types that are allowed to migrate in space and branch locally only if bothtypes are present. We continue our investigation of the large scale behaviourof the system started in Blath, Hammer and Ortgiese (2016), where we showedthat the continuum system converges after diffusive rescaling. Inspired by ascaling property of the continuum model, a series of earlier works initiated byKlenke and Mytnik (2010, 2012) studied the model on a discrete space, but withinfinite branching rate. In this paper, we bridge the gap between the twomodels by showing that by diffusively rescaling this discrete space infiniterate model, we obtain the continuum model from Blath, Hammer and Ortgiese(2016). As an application of this convergence result, we show that if we startthe infinite rate system from complementary Heaviside initial conditions, theinitial ordering of types is preserved in the limit and that the interfacebetween the types consists of a single point.

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