Anomalous scaling regime for one-dimensional Mott variable-range hopping

Abstract: I will present an anomalous, sub-diffusive scaling limit for a one-dimensional version of the Mott random walk, which was originally introduced as a model for electron transport in a disordered medium. The limiting process can be viewed heuristically as a one-dimensional diffusion with an absolutely continuous speed measure and a discontinuous scale function, as given by a two-sided stable subordinator. Corresponding to intervals of low conductance in the discrete model, the discontinuities in the scale function act as barriers off which the limiting process reflects for some time before crossing. A main goal of the talk is to explain the proof strategy, which relies on a recently developed theory that relates the convergence of processes to that of associated resistance metric measure spaces, which has also proved useful for other examples of random walks in random environments.

probability

Audience: researchers in the topic

Probability Victoria Seminar (PVSeminar)

Series comments: All the information about the forthcoming and past events (including the seminars' Zoom links, where available) can be found at probvic.wordpress.com/pvseminar/. The URL of the seminar YouTube channel is: www.youtube.com/channel/UCsEpm-bMfCL2w8abq9s7w6w