  We consider systems of diffusion processes ("particles") interacting through
their ranks (also referred to as "rank-based models" in the mathematical
finance literature). We show that, as the number of particles becomes large,
the process of fluctuations of the empirical cumulative distribution functions
converges to the solution of a linear parabolic SPDE with additive noise. The
coefficients in the limiting SPDE are determined by the hydrodynamic limit of
the particle system which, in turn, can be described by the porous medium PDE.
The result opens the door to a thorough investigation of large equity markets
and investment therein. In the course of the proof we also derive quantitative
propagation of chaos estimates for the particle system.
