Branching Brownian Motion with spatially-homogeneous and point-catalytic branching

TL;DR

This paper studies a Branching Brownian Motion model combining spatially-homogeneous and point-catalytic branching, analyzing population growth rates and the asymptotic behavior of the rightmost particle.

Contribution

It introduces a combined model of branching at a point and throughout space, deriving growth rates and asymptotic behavior of extremal particles.

Findings

Established almost sure growth rates in time-dependent regions

Determined first-order asymptotics of the rightmost particle

Unified analysis of spatially-homogeneous and catalytic branching

Abstract

We consider a model of Branching Brownian Motion in which the usual spatially-homogeneous and catalytic branching at a single point are simultaneously present. We establish the almost sure growth rates of population in certain time-dependent regions and as a consequence the first-order asymptotic behaviour of the rightmost particle.