Exponential inequalities for martingales and asymptotic properties of   the free energy of directed polymers in random environment
  The objective of the present paper is to establish exponential large deviation inequalities, and to use them to show exponential concentration inequalities for the free energy of a polymer in general random environment, its rate of convergence, and an expression of its limit value in terms of those of some multiplicative cascades. 
Quansheng Liu (LMAM), Fr\'ed\'erique Watbled (LMAM)