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

Abstract : 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 $\alpha \in[0,1]$ such that $\log X_n / \log n \to \alpha$. Interestingly, $\alpha$ does not depend on the intensity of the bias in the first case, but it does in the second case.
Keywords :
Type de document :
Pré-publication, Document de travail
12 pages, 1 figure. 2017
Domaine :

Littérature citée [13 références]

https://hal.archives-ouvertes.fr/hal-01635371
Contributeur : Quentin Berger <>
Soumis le : mercredi 15 novembre 2017 - 10:11:23
Dernière modification le : jeudi 11 janvier 2018 - 06:12:30

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Scaling_RWRC.pdf
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• HAL Id : hal-01635371, version 1
• ARXIV : 1711.04676

### Citation

Quentin Berger, Michele Salvi. Scaling of sub-ballistic 1D Random Walks among biased Random Conductances. 12 pages, 1 figure. 2017. 〈hal-01635371〉

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