Anomalous scaling regime for onedimensional Mott variablerange hopping
Abstract
We derive an anomalous, subdiffusive scaling limit for a onedimensional version of the Mott random walk. The limiting process can be viewed heuristically as a onedimensional diffusion with an absolutely continuous speed measure and a discontinuous scale function, as given by a twosided 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. We also discuss how, by incorporating a Bouchaud trap model element into the setting, it is possible to combine this 'blocking' mechanism with one of 'trapping'. Our proof relies on a recently developed theory that relates the convergence of processes to that of associated resistance metric measure spaces.
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 DOI:
 10.48550/arXiv.2010.01779
 arXiv:
 arXiv:2010.01779
 Bibcode:
 2020arXiv201001779C
 Keywords:

 Mathematics  Probability;
 Mathematical Physics;
 60K37 (primary);
 60F17;
 60G52;
 60J27;
 82A41;
 82D30
 EPrint:
 53 pages, 6 figures