Diffusivity in one-dimensional generalized Mott variable-range hopping models

Abstract

We consider random walks in a random environment which are generalized versions of well-known effective models for Mott variable-range hopping. We study the homogenized diffusion constant of the random walk in the one-dimensional case. We prove various estimates on the low-temperature behavior which confirm and extend previous work by physicists.

Published in at http://dx.doi.org/10.1214/08-AAP583 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (5)

• Quenched invariance principle for simple random walk on percolation clusters
• Mott law as lower bound for a random walk in a random environment
• Bulk diffusion of 1D exclusion process with bond disorder
• Isoperimetric inequalities and mixing time for a random walk on a random point process
• Conductance statistics in small GaAs:Si wires at low temperatures. I. Theoretical analysis: truncated quantum fluctuations in insulating wires

Cited by in corpus (5)

• Random walks in a one-dimensional Lévy random environment
• Invariance principle for Mott variable range hopping and other walks on point processes
• Dissipative dynamics in semiconductors at low temperature
• Large fluctuations and transport properties of the Lévy-Lorentz gas
• Anomalous scaling regime for one-dimensional Mott variable-range hopping