# New bounds for the free energy of directed polymers in dimension 1+1 and 1+2

Abstract : We study the free energy of the directed polymer in random environment in dimension 1+1 and 1+2. For dimension 1, we improve the statement of Comets and Vargas concerning very strong disorder by giving sharp estimates on the free energy at high temperature. In dimension 2, we prove that very strong disorder holds at all temperatures, thus solving a long standing conjecture in the field.
Type de document :
Pré-publication, Document de travail
32 pages, 4 figures. 2009
Domaine :

https://hal.archives-ouvertes.fr/hal-00361863
Contributeur : Hubert Lacoin <>
Soumis le : lundi 16 février 2009 - 18:23:40
Dernière modification le : mercredi 21 mars 2018 - 18:56:48

### Identifiants

• HAL Id : hal-00361863, version 1
• ARXIV : 0901.0699

### Citation

Hubert Lacoin. New bounds for the free energy of directed polymers in dimension 1+1 and 1+2. 32 pages, 4 figures. 2009. 〈hal-00361863〉

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