# 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 :
Document type :
Journal articles
Domain :

Cited literature [29 references]

https://hal.archives-ouvertes.fr/hal-01170204
Contributor : Quentin Berger <>
Submitted on : Wednesday, July 1, 2015 - 10:40:08 AM
Last modification on : Friday, March 27, 2020 - 4:01:18 AM
Document(s) archivé(s) le : Tuesday, April 25, 2017 - 9:27:11 PM

### File

DirectedPolymer.pdf
Files produced by the author(s)

### Citation

Quentin Berger, Hubert Lacoin. The high-temperature behavior for the directed polymer in dimension 1+2. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institute Henri Poincaré, 2017, 53 (1), pp.430-450. ⟨10.1214/15-AIHP721⟩. ⟨hal-01170204⟩

Record views