Mutually Catalytic Branching Processes on the Lattice and Voter Processes with Strength of Opinion

Since the seminal work of Dawson and Perkins, mutually catalytic versions of super-processes have been studied frequently. In this article we combine two approaches extending their ideas: the approach of adding correlations to the driving noise of the system is combined with the approach of obtaining new processes by letting the branching rate tend to infinity. We introduce infinite rate symbiotic branching processes which surprisingly can be interpreted as generalized voter processes with additional strength of opinions. Since many of the arguments go along the lines of known proofs this article is written as a review article.

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Source https://hal.science/hal-00706810
Author Doering, Leif, Mytnik, Leonid
Maintainer CCSD
Last Updated May 15, 2026, 20:09 (UTC)
Created May 15, 2026, 20:09 (UTC)
Identifier hal-00706810
Language en
contributor Laboratoire de Probabilités et Modèles Aléatoires (LPMA) ; Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
creator Doering, Leif
date 2011-12-22T00:00:00
harvest_object_id 995ee5c3-2d25-4da3-b2b6-3a66f1c4e7e3
harvest_source_id 3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title test moissonnage SELUNE
metadata_modified 2025-09-29T00:00:00
relation info:eu-repo/semantics/altIdentifier/arxiv/1109.6106
set_spec type:UNDEFINED