Branching Brownian motion: Almost sure growth along scaled paths

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.

21 pages, 1 figure. Corrected definition of rate function and other typos.