Limiting distributions for particles near the frontier of spatially inhomogeneous branching Brownian motions

TL;DR

This paper studies the limiting distribution and growth rate of particles near the frontier in two-dimensional inhomogeneous branching Brownian motions with a Kato class measure, providing insights into their asymptotic behavior.

Contribution

It introduces a novel analysis of particle distributions near the frontier in 2D inhomogeneous branching Brownian motions with Kato class branching rates.

Findings

Derived the limiting distribution of particles near the frontier

Established the evolution rate of particles in the model

Focused on the two-dimensional case with compact support measures

Abstract

Our purpose in this paper is to determine the limiting distribution and the evolution rate of particles near the frontier of branching Brownian motions. Here the branching rate is given by a Kato class measure with compact support in Euclidean space. Our investigation focuses on the two dimensional case.