On the critical point of the Random Walk Pinning Model in Dimension d=3

Résumé : We consider the Random Walk Pinning Model studied in [Birkner-Sun 2008] and [Birkner-Greven-den Hollander 2008]: this is a random walk X on Z^d, whose law is modified by the exponential of beta times the collision local time up to time N with the (quenched) trajectory Y of another d-dimensional random walk. If β exceeds a certain critical value βc, the two walks stick together for typical Y realizations (localized phase). A natural question is whether the disorder is relevant or not, that is whether the quenched and annealed systems have the same critical behavior. Birkner and Sun proved that βc coincides with the critical point of the annealed Random Walk Pinning Model if the space dimension is d=1 or d=2, and that it differs from it in dimension d larger or equal to 4 (for d strictly larger than 4, the result was proven also in [Birkner-Greven-den Hollander 2008]). Here, we consider the open case of the marginal dimension d=3, and we prove non-coincidence of the critical points.
Type de document :
Article dans une revue
Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2010, 15 (21), pp.654-683. <10.1214/EJP.v15-761>
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01426326
Contributeur : Quentin Berger <>
Soumis le : mercredi 4 janvier 2017 - 13:39:17
Dernière modification le : lundi 29 mai 2017 - 14:22:17
Document(s) archivé(s) le : mercredi 5 avril 2017 - 13:59:43

Fichier

dim3_modif0204.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Quentin Berger, Fabio Toninelli. On the critical point of the Random Walk Pinning Model in Dimension d=3. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2010, 15 (21), pp.654-683. <10.1214/EJP.v15-761>. <hal-01426326>

Partager

Métriques

Consultations de
la notice

109

Téléchargements du document

27