The high-temperature behavior for the directed polymer in dimension 1+2

Abstract : We investigate the high-temperature behavior of the directed polymer model in dimension 1+2. More precisely we study the difference $\Delta F (\beta)$ between the quenched and annealed free energies for small values of the inverse temperature $\beta$. This quantity is associated to localization properties of the polymer trajectories, and is related to the overlap fraction of two replicas. Adapting recent techniques developed by the authors in the context of the disordered pinning model (Berger and Lacoin, arXiv:1503.07315 [math-ph]), we identify the sharp asymptotic high temperature behavior \[ \lim_{\beta\to0} \beta^2 \log \Delta F (\beta) = -\pi . \]
Type de document :
Pré-publication, Document de travail
2015
Liste complète des métadonnées


https://hal.archives-ouvertes.fr/hal-01170204
Contributeur : Quentin Berger <>
Soumis le : mercredi 1 juillet 2015 - 10:40:08
Dernière modification le : vendredi 28 avril 2017 - 01:02:46
Document(s) archivé(s) le : mardi 25 avril 2017 - 21:27:11

Fichier

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

Identifiants

Collections

Citation

Quentin Berger, Hubert Lacoin. The high-temperature behavior for the directed polymer in dimension 1+2. 2015. <hal-01170204>

Partager

Métriques

Consultations de
la notice

69

Téléchargements du document

32