The Gini reveals more

title: Branching Brownian motion with selection
The branching Brownian motion (BBM) can be seen as a system of diffusing and
reproducing particles. It can also be regarded as a tree-indexed Brownian motion,
thereby joining two fundamental concepts in probability theory: Brownian motion and
random trees.
In this talk I will present some results obtained in my thesis (arXiv:1210.3500) about a
model of one-dimensional BBM with selection, called the N-BBM. In this model, as soon
as the number of particles exceeds a (large) given number N, only the N right-most
particles are kept (space is drawn horizontally), the others being removed from the
system. I will expose some precise estimates on the position of the cloud of particles for
large N. More precisely, I show that it converges in law at the time-scale log^3 N to a
Lévy process, thereby justifying results obtained by the physicists Brunet, Derrida,
Mueller and Munier through PDE methods. I will explain as well how this study
contributes to the understanding of the so-called noisy FKPP equation.