The seminar is sponsored by NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai.
Abstract:
We consider the following conservative particle system: N particles move on the line driven by independent brownian motions. In addition, at rate N two particles are chosen and the leftmost one jumps over the position of the rightmost one. This is a slight modification of one of the process considered by Brunet and Derrida to study the shift in the velocity of a front due to microscopic effects. For this system, we will prove propagation of chaos that leads to a hydrodynamic limit: the empirical cumulative distribution of the particles converges to a (deterministic) solution of the F-KPP equation. As a consequence we obtain that the cloud of particles travels at a velocity v_N that converges to the minimal velocity of the equation.
Biography:
Pablo Groisman is a Visiting Associate Professor of Mathematics at NYU Shanghai. He is also a tenured researcher at CONICET-Argentina and Professor at University of Buenos Aires. His research interests include stochastic processes, interacting particle systems and conditioned evolution.