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Main Title: The infinite rate symbiotic branching model: from discrete to continuous space
Author(s): Hammer, Matthias
Ortgiese, Marcel
Type: Research Paper
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.
Subject(s): symbiotic branching model
mutually catalytic branching
stepping stone model
rescaled interface
moment duality
Meyer-Zheng topology
Issue Date: 13-May-2015
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 60K35 Interacting random processes; statistical mechanics type models; percolation theory
60J80 Branching processes
60H15 Stochastic partial differential equations
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2015, 08
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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