Branching diffusion in the super-critical regime

TL;DR

This paper studies the long-term behavior of super-critical branching diffusion processes in inhomogeneous media, focusing on particle growth, spatial distribution, and region expansion over time.

Contribution

It provides a detailed analysis of the asymptotic behavior and spatial growth of branching diffusion processes in the super-critical regime, which was previously less understood.

Findings

Particles grow exponentially with positive probability.

The spatial distribution of particles can be characterized asymptotically.

The occupied region expands over time in a quantifiable manner.

Abstract

We investigate the long-time evolution of branching diffusion processes (starting with a single particle) in inhomogeneous media. The qualitative behavior of the processes depends on the intensity of the branching. We analyze the super-critical case, when the total number of particles growing exponentially with positive probability. We study the asymptotics of the number of particles in different regions of space and describe the growth of the region occupied by the particles.