Branching Brownian motion: Almost sure growth along scaled paths

TL;DR

This paper proves a result on the almost sure growth of particles in branching Brownian motion along scaled paths, using probabilistic methods and spine techniques inspired by large deviations theory.

Contribution

It introduces a new probabilistic approach employing spine techniques to analyze growth along paths in branching Brownian motion.

Findings

Established almost sure growth rates along scaled paths

Applied modern spine techniques to branching processes

Connected large deviations principles with particle growth analysis

Abstract

We give a proof of a result on the growth of the number of particles along chosen paths in a branching Brownian motion. The work follows the approach of classical large deviations results, in which paths in $C[0,1]$ are rescaled onto $C[0,T]$ for large $T$. The methods used are probabilistic and take advantage of modern spine techniques.