- 03-37 A. Faggionato
- Hydrodynamic limit of a disordered system (Ph.D. Thesis)
(811K, Postscript .gz)
Feb 6, 03
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Abstract. We study the motion of free electrons in a doped crystal by means
of a lattice gas whose particles interact only by mutual exclusion
and perform random walks on Z^d with jump rates depending locally
on a disorder field given by i.i.d. bounded variables.
We prove the almost sure existence of the hydrodynamic limit in
dimensions d>2. The limit equation is a non linear diffusion equation
whose diffusion matrix does not depend on the realization of the
disorder field and admits a variational characterization.