## On some large systems of random particles which approximate scalar conservation laws.(English)Zbl 0846.35081

Summary: We build an $$N$$-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 $$L^1$$ distance between the one-particle density function and its kinetic limit, using an appropriate joint process.

### MSC:

 35L65 Hyperbolic conservation laws