  In this paper we consider an interacting particle system in $\mathbb{R}^d$
modelled as a system of $N$ stochastic differential equations driven by L\'evy
processes. The limiting behaviour as the size $N$ grows to infinity is achieved
as a law of large numbers for the empirical density process associated with the
interacting particle system. We prove that the empirical process converges,
uniformly in the space variable, to the solution of the $d$-dimensional fractal
conservation law.
