# 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 $\lim_{\beta\to0} \beta^2 \log \Delta F (\beta) = -\pi .$
Keywords :
Type de document :
Pré-publication, Document de travail
2015
Domaine :

https://hal.archives-ouvertes.fr/hal-01170204
Contributeur : Quentin Berger <>
Soumis le : mercredi 1 juillet 2015 - 10:40:08
Dernière modification le : mardi 11 octobre 2016 - 15:20:19

### Fichier

DirectedPolymer.pdf
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### Citation

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

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