# 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.
Document type :
Preprints, Working Papers, ...
32 pages, 4 figures. 2009
Domain :

https://hal.archives-ouvertes.fr/hal-00361863
Contributor : Hubert Lacoin <>
Submitted on : Monday, February 16, 2009 - 6:23:40 PM
Last modification on : Tuesday, May 30, 2017 - 1:07:54 AM

### Identifiers

• 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>

### Metrics

Consultations de la notice