# Limiting distribution of particles near the frontier in the catalytic branching Brownian motion

## TL;DR

This paper investigates the asymptotic distribution of particles in catalytic branching Brownian motion with a focus on particles near the critical speed, providing detailed insights into their spatial distribution and growth behavior.

## Contribution

It offers new precise results on the asymptotic behavior and spatial distribution of particles in catalytic branching Brownian motion, especially at the critical speed.

## Key findings

- Asymptotic behavior of particle numbers at different speeds
- Explicit characterization of particles at the critical speed
- Detailed spatial distribution results

## Abstract

We consider the model of branching Brownian motion with a single catalytic point at the origin and binary branching. We establish some fine results for the asymptotic behaviour of the numbers of particles travelling at different speeds and give an explicit characterisation of the spatial distribution of particles travelling at the critical speed.