  We investigate the behavior of systems of interacting diffusion processes,
known as volatility-stabilized market models in the mathematical finance
literature, when the number of diffusions tends to infinity. We show that,
after an appropriate rescaling of the time parameter, the empirical measure of
the system converges to the solution of a degenerate parabolic partial
differential equation. A stochastic representation of the latter in terms of
one-dimensional distributions of a time-changed squared Bessel process allows
us to give an explicit description of the limit.
