  The nonlocal porous medium equation considered in this paper is a degenerate
nonlinear evolution equation involving a space pseudo-differential operator of
fractional order. This space-fractional equation admits an explicit,
nonnegative, compactly supported weak solution representing a probability
density function. In this paper we analyze the link between isotropic transport
processes, or random flights, and the nonlocal porous medium equation. In
particular, we focus our attention on the interpretation of the weak solution
of the nonlinear diffusion equation by means of random flights.
