Stochastic homogenization in amorphous media and applications to Mott variable range hopping.

10 Apr 2019, 11:00
50m
Villa Finaly

Villa Finaly

Via Bolognese, 134 R 50139 Florence Italy

Speaker

Alessandra Faggionato

Description

By extending the method of 2-scale convergence we prove an homogenization theorem of difference operators given by Markov generators of random walks on random marked simple point processes with symmetric jump rates. Using this theorem, we derive two further results: (i) the hydrodynamic limit of the exclusion process given by multiple random walks with hard-core interaction; (ii) the a.s. convergence of the rescaled conductivity matrix of the Miller-Abrahams resistor network to the diffusion matrix of Mott random walk. The second result is related to Mott variable range hopping, which is a fundamental mechanism of phonon-induced electron conduction in amorphous solids given by strongly disordered solids as doped semiconductors.

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