 04229 A. Faggionato, H. SchulzBaldes, D. Spehner
 Mott law as lower bound for a random walk in a random environment
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Jul 26, 04

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Abstract. We consider a random walk on the support of a stationary simple point
process on $R^d$, $d\geq 2$ which satisfies a mixing condition w.r.t.the
translations or has a strictly positive density uniformly on large enough
cubes. Furthermore the point process is furnished with independent random
bounded energy marks. The transition rates of the random walk decay
exponentially in the jump distances and depend on the energies through a
factor of the Boltzmanntype. This is an effective model for the
phononinduced hopping of electrons in disordered solids within the regime of strong Anderson localization. We show that the rescaled random walk converges to a Brownian motion whose diffusion coefficient is bounded below by Mott's law for the variable range hopping conductivity at zero
frequency. The proof of the lower bound involves estimates for the
supercritical regime of an associated site percolation problem.
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