On some large systems of random particles which approximate scalar conservation laws

Abstract

We build aN-particle stochastic system subject to a multibody interaction. The postcollisional repartition is performed so that the one-particle density function solves a scalar conservation law in a suitable limit of hydrodynamical type. In the kinetic limit, we recover a relaxation model which approximates the scalar. conservation. law. Our proof relies on a direct estimate of the L¹ distance between the one-particle density function and its kinetic limit, using an appropriate joint process.