Extremal regime for one-dimensional Mott variable-range hopping
Annales Henri Lebesgue, Volume 6 (2023), pp. 1169-1211.


Keywords random walk in random environment, disordered media, sub-diffusivity, Mott variable-range hopping, extremal process


We study the asymptotic behaviour of a version of the one-dimensional Mott random walk in a regime that exhibits severe blocking. We establish that, for any fixed time, the appropriately-rescaled Mott random walk is situated between two environment-measurable barriers, the locations of which are shown to have an extremal scaling limit. Moreover, we give an asymptotic description of the distribution of the Mott random walk between the barriers that contain it.


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