  We construct a nearest-neighbour interacting particle system of exclusion
type, which illustrates a transition from slow to fast diffusion. More
precisely, the hydrodynamic limit of this microscopic system in the diffusive
space-time scaling is the parabolic equation $\partial_t\rho=\nabla
(D(\rho)\nabla \rho)$, with diffusion coefficient $ D(\rho)=m\rho^{m-1} $ where
$ m\in(0,2] $, including therefore the fast diffusion regime in the range $
m\in(0,1) $, and the porous {medium} equation for $ m\in(1,2) $. The
construction of the model is based on the generalized binomial theorem, and
interpolates continuously in $ m $ the already known microscopic porous medium
model with parameter $ m=2 $, the symmetric simple exclusion process with $ m=1
$, going down to a fast diffusion model up to any $ m>0$. The derivation of the
hydrodynamic limit for the local density of particles on the one-dimensional
torus is achieved via the entropy method -- with additional technical
difficulties depending on the regime (slow or fast diffusion) and where new
properties of the porous medium model need to be derived.
