Exponential inequalities for martingales and asymptotic properties of the free energy of directed polymers in random environment

Quansheng Liu, Frédérique Watbled

Published 2008-12-09Version 1

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.