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Scaling of sub-ballistic 1D Random Walks among biased Random Conductances

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Date
2017
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-01635371
Dewey
Probabilités et mathématiques appliquées
Sujet
Random walk; Random environment; Limit theorems; Conductance model; Mott random walk
URI
https://basepub.dauphine.fr/handle/123456789/17527
Collections
  • CEREMADE : Publications
Metadata
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Author
Berger, Quentin
102 Laboratoire de Probabilités et Modèles Aléatoires [LPMA]
Salvi, Michele
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Document de travail / Working paper
Item number of pages
12
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.

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