Title: Macroscopic diffusion from a Hamilton-like dynamics

Abstract:
We introduce and analyze a model for the transport of particles or 
energy in extended lattice systems. The dynamics of the model has all 
the properties of Hamiltonian dynamics in a confined phase space : it is 
deterministic, periodic, reversible and conservative. Randomness enters 
the model as a way to model ignorance about initial conditions and 
interactions between the components of the system. The orbits of the 
particles are non-intersecting random loops.
We prove, as a weak law of large number, the validity of a diffusion 
equation for the macroscopic observables of interest for time arbitrary 
large, but small compared to the minimal recurrence time in the 
dynamics.