Julián Martinez (UBA)

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.

Departamento de Matemáticas

Pontificia Universidad Católica de Chile (PUC-Chile)

Av. Vicuña Mackenna 4860, Macul,

Santiago – Chile

(+56 2) 2354 5779

Centro de Modelamiento Matemático (CMM)

Facultad de Ciencias Físicas y Matemáticas (FCFM)

Universidad de Chile

Beauchef 851, Edificio Norte, Piso 7,

Santiago – Chile