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Article Dans Une Revue Markov Processes And Related Fields Année : 2019

Scaling of Sub-Ballistic 1D Random Walks Among Biased Random Conductances

Résumé

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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Dates et versions

hal-01635371 , version 1 (15-11-2017)
hal-01635371 , version 2 (21-11-2018)

Identifiants

Citer

Quentin Berger, Michele Salvi. Scaling of Sub-Ballistic 1D Random Walks Among Biased Random Conductances. Markov Processes And Related Fields, 2019, 25 (1), pp.171-187. ⟨hal-01635371v2⟩
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