Scaling of Sub-Ballistic 1D Random Walks Among Biased Random Conductances - INRAE - Institut national de recherche pour l’agriculture, l’alimentation et l’environnement Access content directly
Journal Articles Markov Processes And Related Fields Year : 2019

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 Undefined control sequence \ga such that Undefined control sequence \ga. Interestingly, Undefined control sequence \ga does not depend on the intensity of the bias in the first case, but it does in the second case. %Moreover, with additional information on the distribution of the conductances, we are able to identify more sharply the correct scaling, and the limiting distribution for the rescaled Xn.
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Dates and versions

hal-02619727 , version 1 (25-05-2020)

Identifiers

  • HAL Id : hal-02619727 , version 1
  • PRODINRA : 472688
  • WOS : 000468336300007

Cite

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-02619727⟩
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