Francis Comets, Tokuzo Shiga, Nobuo Yoshida
Directed Polymers in Random Environment: 
Path Localization and Strong Disorder
(46K, LaTex2e)

ABSTRACT.  We consider directed polymers in random environment. 
Under mild assumptions on the environment, we prove here: 
(i) equivalence of decay rate of the partition 
function with some natural localization properties 
of the path, (ii) quantitative estimates of the decay 
of the partition function in dimensions one or two, 
or at sufficiently low temperature, 
(iii) existence of quenched free energy. 
In particular, we generalize to general environments, 
some of the results recently obtained by 
P. Carmona and Y. Hu for a Gaussian environment. 
We do not discuss here superdiffusivity or critical exponents.