# 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.
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https://hal.archives-ouvertes.fr/hal-01635371
Contributor : Quentin Berger <>
Submitted on : Wednesday, November 21, 2018 - 11:39:20 AM
Last modification on : Monday, May 25, 2020 - 8:30:03 PM
Document(s) archivé(s) le : Friday, February 22, 2019 - 1:16:08 PM

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Scaling_RWRC_revision.pdf
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### Identifiers

• HAL Id : hal-01635371, version 2
• ARXIV : 1711.04676

### Citation

Quentin Berger, Michele Salvi. Scaling of sub-ballistic 1D Random Walks among biased Random Conductances. 2018. ⟨hal-01635371v2⟩

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