Consider the partition function of a directed polymer in ℤd, d≥1, in an IID field. We assume that both tails of the negative and the positive part of the field are at least as light as exponential. It is well known that the free energy of the polymer is equal to a deterministic constant for almost every realization of the field and that the upper tail of the large deviations is exponential. The lower tail of the large deviations is typically lighter than exponential. In this paper we obtain sharp estimates on the lower tail of the large deviations given in terms of the distribution of the IID field. Our proofs are also applicable to the model of directed last passage percolation and (non-directed) first passage percolation.
Publié le : 2009-08-15
Classification:
Large deviations,
Partition function,
Last passage percolation,
60K35,
60F10
@article{1249391384,
author = {Ben-Ari, Iddo},
title = {Large deviations for partition functions of directed polymers in an IID field},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {45},
number = {1},
year = {2009},
pages = { 770-792},
language = {en},
url = {http://dml.mathdoc.fr/item/1249391384}
}
Ben-Ari, Iddo. Large deviations for partition functions of directed polymers in an IID field. Ann. Inst. H. Poincaré Probab. Statist., Tome 45 (2009) no. 1, pp. 770-792. http://gdmltest.u-ga.fr/item/1249391384/