Stochastic homogenization in amorphous media and applications to interacting particle systems and random resistor networks

We consider random walks on marked simple point processes with symmetric jump rates and unbounded jump range. Examples are given by simple random walks on Delaunay triangulations or Mott variable range hopping in doped semiconductors. We present homogenization results for the associated Markov generators. As a first application, we obtain the hydrodynamic limit of the exclusion process given by multiple random walks as above, with hard–core interaction. As a second application, we derive a limit theorem for the effective conductivity of some classes of random resistor networks. This result together with a percolation-type analysis allows to derive the low temperature scaling behavior of conductivity in some classes of strongly disordered media.