  We recover the so-called field-road diffusion model as the hydrodynamic limit
of an interacting particle system. The former consists of two parabolic PDEs
posed on two sets of different dimensions (a "field" and a "road" in a
population dynamics context), and coupled through exchange terms between the
field's boundary and the road. The latter stands as a Symmetric Simple
Exclusion Process (SSEP): particles evolve on two microscopic lattices
following a Markov jump process, with the constraint that each site cannot host
more than one particle at the same time. The system is in contact with
reservoirs that allow to create or remove particles at the boundary sites. The
dynamics of these reservoirs are slowed down compared to the diffusive
dynamics, to reach the reactions and the boundary conditions awaited at the
macroscopic scale. This issue of bridging two spaces of different dimensions
is, as far as we know, new in the hydrodynamic limit context, and raises
perspectives towards future related works.
