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

TL;DR

This paper reviews the development of mutually catalytic super-processes, introduces infinite rate symbiotic branching processes, and interprets them as generalized voter models with enhanced opinion strength.

Contribution

It combines correlation-based noise approaches with infinite branching rate limits to create new processes interpreted as voter models with stronger opinions.

Findings

Introduction of infinite rate symbiotic branching processes

Interpretation as generalized voter processes with opinion strength

Connection of correlation methods with infinite branching limits

Abstract

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.