2011, Roberts, Matthew I.

We give proofs of two results about the position of the extremal particle in a branching Brownian motion, one concerning the median position and another the almost sure behaviour. Our methods are based on a many-to-two lemma which allows us to estimate the effect of the branching structure on the system by considering two dependent Bessel processes.

2011, Harris, Simon S., Roberts, Matthew I.

We develop an extension to the spine theory of branching processes, and use it to give a simple and intuitive identity for calculating additive functionals of such processes, generalizing the well-known many-to-one lemma.