We consider the following system in the Brunet-Derrida class: Take N

particles on the real line, each of which performs a Brownian motion

independently of any other. At rate 1/(N-1) two particles are chosen at

random, the one with the biggest position branches into two particles

and the one with the smallest position dies.

We will show that the empirical cumulative distribution associated to

this process converges in probability to the solution of the KPP

equation. Throughout the proof propagation of chaos is shown, whenever

N tends to infinity.

Additionally, for each N, we prove existence of a velocity for the

cloud of particles and a lower bound for its limit in N. Such a bound

turns out to be the minimal velocity for the KPP equation. Joint work

with Pablo Groisman and Matthieu Jonckheere.

Pontificia Universidad Católica de Chile (PUC-Chile)

Av. Vicuña Mackenna 4860, Macul,

Santiago – Chile

(+56 2) 2354 5779

Facultad de Ciencias Físicas y Matemáticas (FCFM)

Universidad de Chile

Beauchef 851, Edificio Norte, Piso 7,

Santiago – Chile