The seminar is sponsored by NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai.
Abstract:
We study a system of Brownian particles interacting through their rank. Initially, the particles are distributed as the marks of a Poisson point process of rate \lambda in (0,\infty), while the negative axis (-\infty,0) is empty. As time runs, the particles perform independent Brownian Motions on \R. The interaction comes from the fact that the (current) left-most particle gets a constant drift to the right. We identify the Hydrodynamic limit of the system as a free-boundary problem: the one-phase Stefan problem. Via this solution we explicitly determine the limiting particle-density profile as well as the asymptotic trajectory of the left-most particle. In particular, we see that if the density of particles \lambda is high, the leftmost particle is transient to the left, whereas, if \lambda is small, the leftmost particle is transient to the right.
Joint work with A. Dembo, A. Sarantsev and V. Sidoravicius.
Biography:
Manuel Cabezas is a Professor at Pontificia Universidad Católica de Chile. His research interests are diffusions in disordered media and interacting particle systems.