Rescaling the spatial lambda Fleming-Viot process and convergence to super-Brownian motion

TL;DR

This paper demonstrates that a rescaled spatial Lambda-Fleming-Viot process converges to super-Brownian motion, extending previous results by removing impact factor restrictions, especially relevant in two-dimensional biological models.

Contribution

It extends prior convergence results by allowing impact factors to remain non-vanishing, broadening the applicability to biologically relevant scenarios.

Findings

Convergence of rescaled process to super-Brownian motion

Extension of previous results to non-vanishing impact factors

Relevance to two-dimensional biological models

Abstract

We show that a space-time rescaling of the spatial Lamba-Fleming-Viot process of Barton and Etheridge converges to super-Brownian motion. This can be viewed as an extension of a result of Chetwynd-Diggle and Etheridge (2018). In that work the scaled impact factors (which govern the event based dynamics) vanish in the limit, here we drop that requirement. The analysis is particularly interesting in the biologically relevant two-dimensional case.