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

Abstract

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.

25 pages

References in corpus (1)

• On Hoeffding's inequalities

Cited by in corpus (14)

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• Pinning, diffusive fluctuations, and Gaussian limits for half-space directed polymer models
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• Number of paths in oriented percolation as zero temperature limit of directed polymer
• The Multiplicative Version of Azuma's Inequality, with an Application to Contention Analysis
• Two-sided bounds on free energy of directed polymers on strongly recurrent graphs
• Some deviation inequalities for sums of negatively associated random variables
• Free energy of directed polymers in random environment in $1+1$-dimension at high temperature
• A variational formula for large deviations in First-passage percolation under tail estimates
• An exponential inequality for orthomartingale differences random fields and some applications