Renormalization of the two-dimensional Lotka--Volterra model

TL;DR

This paper demonstrates that near criticality, the two-dimensional Lotka--Volterra model, when properly renormalized, converges to a super-Brownian motion, providing insights into the model's long-term behavior.

Contribution

It establishes the convergence of the renormalized two-dimensional Lotka--Volterra model to super-Brownian motion and links this to the survival of a rare type near the voter model.

Findings

Convergence to super-Brownian motion near criticality

Long-term survival of a rare type for certain parameters

Connection to voter model dynamics

Abstract

We show that renormalized two-dimensional Lotka--Volterra models near criticality converge to a super-Brownian motion. This is used to establish long-term survival of a rare type for a range of parameter values near the voter model.