A simple path to asymptotics for the frontier of a branching Brownian motion

TL;DR

This paper provides concise proofs of classical results regarding the extremal particle's position in branching Brownian motion, focusing on median position and almost sure behavior.

Contribution

It offers simplified proofs of key asymptotic properties of the extremal particle in branching Brownian motion.

Findings

Median position of extremal particle characterized

Almost sure behavior of extremal particle established

Simplified proofs of classical results provided

Abstract

We give short proofs of two classical results about the position of the extremal particle in a branching Brownian motion, one concerning the median position and another the almost sure behaviour.