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Scaling of sub-ballistic 1D Random Walks among biased Random Conductances: a story of wells and walls

Berger, Quentin; Salvi, Michele (2020), Scaling of sub-ballistic 1D Random Walks among biased Random Conductances: a story of wells and walls, Electronic Journal of Probability, 25, p. 1-43. 10.1214/20-EJP427

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Type
Article accepté pour publication ou publié
Date
2020
Journal name
Electronic Journal of Probability
Volume
25
Publisher
Institute of Mathematical Statistics
Pages
1-43
Publication identifier
Metadata
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Author(s)
Berger, Quentin
Laboratoire de Probabilités, Statistique et Modélisation [LPSM (UMR_8001)]
Salvi, Michele
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We consider two models of one-dimensional random walks among biased i.i.d. random conductances: the first is the classical exponential tilt of the conductances, while the second comes from the effect of adding an external field to a random walk on a point process (the bias depending on the distance between points). We study the case when the walk is transient to the right but sub-ballistic, and identify the correct scaling of the random walk: we find α∈[0,1] such that logXn/logn→α. Interestingly, α does not depend on the intensity of the bias in the first case, but it does in the second case.
Subjects / Keywords
Mott random walk; Random walk; random environment; limit theorems; conductance model