  For large systems of Brownian particles interacting through their ranks
introduced in (Banner, Fernholz, Karatzas, 2005), the empirical cumulative
distribution function satisfies a porous medium PDE. However, when we introduce
a common noise, the limit is no longer deterministic. Instead, we show that
this limit is a solution of a stochastic PDE related to this porous medium PDE.
This stochastic PDE is somewhat similar to the equations developed for
conservation laws with rough stochastic fluxes (Lions, Perthame, Souganidis,
2013).
