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In this paper, we analyse the rate of convergence of a system of $N$interacting particles with mean-field rank based interaction in the driftcoefficient and constant diffusion coefficient. We first adapt arguments byKolli and Shkolnikhov to check trajectorial propagation of chaos with optimalrate $N^{-1/2}$ to the associated stochastic differential equations nonlinearin the sense of McKean. We next relax the assumptions needed by Bossy to checkconvergence in $L^1(\mathbb{R})$ with rate ${\mathcal O}(\frac{1}{\sqrt N} +h)$ of the empirical cumulative distribution function of the Eulerdiscretization with step $h$ of the particle system to the solution of a onedimensional viscous scalar conservation law. Last, we prove that the bias ofthis stochastic particle method behaves in ${\mathcal O}(\frac{1}{N} + h)$. Weprovide numerical results which confirm our theoretical estimates.

Weak and strong error analysis for mean-field rank based particle approximations of one dimensional viscous scalar conservation law