Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Strong disorder in semidirected random polymers

N. Zygouras

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We consider a random walk in a random potential, which models a situation of a random polymer and we study the annealed and quenched costs to perform long crossings from a point to a hyperplane. These costs are measured by the so called Lyapounov norms. We identify situations where the point-to-hyperplane annealed and quenched Lyapounov norms are different. We also prove that in these cases the polymer path exhibits localization.


Nous considérons une marche aléatoire dans un potentiel aléatoire qui modèle la situation d’un polymère aléatoire et nous étudions les coûts “annealed” et “quenched” pour réaliser de longues traversées d’un point à un hyperplan. Ces coûts sont mesurés en terme de normes de Lyapounov. Nous identifions des situations où les normes de Lyapounov d’un point à un hyperplan “annealed” et “quenched” sont différentes. Nous démontrons également que dans ces cas le chemin du polymère présente une localisation.

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Ann. Inst. H. Poincaré Probab. Statist., Volume 49, Number 3 (2013), 753-780.

First available in Project Euclid: 2 July 2013

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Random walks Random potential Lyapounov norms Strong disorder Localization Fractional moments


Zygouras, N. Strong disorder in semidirected random polymers. Ann. Inst. H. Poincaré Probab. Statist. 49 (2013), no. 3, 753--780. doi:10.1214/12-AIHP483.

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