Scaling limits for sub-ballistic biased random walks in random conductances. (English) Zbl 1430.60089
Summary: We consider biased random walks in positive random conductances on the \(d\)-dimensional lattice in the zero-speed regime and study their scaling limits. We obtain a functional law of large numbers for the position of the walker, properly rescaled. Moreover, we state a functional central limit theorem where an atypical process, related to the fractional kinetics, appears in the limit.
MSC:
| 60K37 | Processes in random environments |
| 82D30 | Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) |
Keywords:
random walks in random environments; random conductances; scaling limit; trap model; zero-speedReferences:
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