Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Perturbing transient random walk in a random environment with cookies of maximal strength

Elisabeth Bauernschubert

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We consider a left-transient random walk in a random environment on $\mathbb{Z}$ that will be disturbed by cookies inducing a drift to the right of strength 1. The number of cookies per site is i.i.d. and independent of the environment. Criteria for recurrence and transience of the random walk are obtained. For this purpose we use subcritical branching processes in random environments with immigration and formulate criteria for recurrence and transience for these processes.


Nous considérons une marche aléatoire unidimensionnelle en environnement aléatoire qui est transiente à gauche. Cette marche est modifiée par des cookies qui induisent une dérive vers la droite. Le nombre de cookies par site est i.i.d. et indépendant de l’environnement. Des critères pour la récurrence et la transience de la marche sont obtenus. Pour cela, nous utilisons des processus de branchement sous-critiques en environnement aléatoire avec immigration et nous formulons des critères de récurrence et de transience pour ces processus.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 49, Number 3 (2013), 638-653.

First available in Project Euclid: 8 August 2013

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Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J85: Applications of branching processes [See also 92Dxx] 60K37: Processes in random environments

Excited random walk in a random environment Cookies of strength 1 Recurrence Transience Subcritical branching process in a random environment with immigration


Bauernschubert, Elisabeth. Perturbing transient random walk in a random environment with cookies of maximal strength. Ann. Inst. H. Poincaré Probab. Statist. 49 (2013), no. 3, 638--653. doi:10.1214/12-AIHP479.

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