Exponential inequalities for martingales and asymptotic properties of the free energy of directed polymers in random environment
arXiv:0812.1719 · doi:10.1016/j.spa.2009.05.001
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.
arXiv comment25 pages
References in corpus (2)
Cited by in corpus (24)
- New bounds for the free energy of directed polymers in dimension 1+1 and 1+2
- Large deviation rate functions for the partition function in a log-gamma distributed random potential
- Localization of directed polymers with general reference walk
- Sharp moment estimates for polynomial martingales
- Partitioning a macroscopic system into independent subsystems
- Sharp asymptotics for the free energy of 1+1 dimensional directed polymers in an infinitely divisible environment
- Self-normalized Cramér type moderate deviations for martingales and applications
- Non-asymptotic Error Bounds For Constant Stepsize Stochastic Approximation For Tracking Mobile Agents
- Moment and tail estimates for martingales and martingale transform, with application to the martingale limit theorem in Banach spaces
- Directed polymers on infinite graphs
- Concentration inequalities for disordered models
- Tail estimates for martingale under "LLN" norming sequence
- On the affine random walk on the torus
- Pinning, diffusive fluctuations, and Gaussian limits for half-space directed polymer models
- 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
- Localization and free energy asymptotics in disordered statistical mechanics and random growth models
- Large deviation inequalities for martingales in Banach spaces
- Two-sided bounds on free energy of directed polymers on strongly recurrent graphs
- Rate of convergence for polymers in a weak disorder
- A variational formula for large deviations in First-passage percolation under tail estimates
- An exponential inequality for orthomartingale differences random fields and some applications
- Some deviation inequalities for sums of negatively associated random variables
- Free energy of directed polymers in random environment in -dimension at high temperature