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Stochastic homogenization in amorphous media and applications to exclusion processes

With Alessandra Faggionato (La Sapienza, Rome)

Stochastic homogenization in amorphous media and applications to exclusion processes

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, which is a fundamental mechanism of phonon–induced electron conduction in amorphous solids as doped semiconductors. We present homogenization results for the associated Markov generators. As an application, we derive the hydrodynamic limit of the simple exclusion process given by multiple random walks as above, with hard–core interaction, on a marked Poisson point process.

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