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

Mathematics – Probability

Scientific paper

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25 pages

Scientific paper

10.1016/j.spa.2009.05.001

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.

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