Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Biased random walks on the interlacement set

Alexander Fribergh and Serguei Popov

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We study a biased random walk on the interlacement set of $\mathbb{Z}^{d}$ for $d\geq3$. Although the walk is always transient, we can show, in the case $d=3$, that for any value of the bias the walk has a zero limiting speed and actually moves slower than any power.


Nous étudions la marche biaisée sur un entrelac aléatoire de $\mathbb{Z}^{d}$ avec $d\geq3$. Nous montrons que la marche est transiente mais que, dans le cas $d=3$, elle est sous-ballistique pour toutes les valeurs du biais et que ses déplacements sont inférieurs à n’importe quel polynôme.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 54, Number 3 (2018), 1341-1358.

Received: 19 October 2016
Revised: 11 April 2017
Accepted: 24 April 2017
First available in Project Euclid: 11 July 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K37: Processes in random environments
Secondary: 60G50: Sums of independent random variables; random walks 82C41: Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50]

Random walk in random environment Interlacement set


Fribergh, Alexander; Popov, Serguei. Biased random walks on the interlacement set. Ann. Inst. H. Poincaré Probab. Statist. 54 (2018), no. 3, 1341--1358. doi:10.1214/17-AIHP841.

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