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Fluctuation exponents and large deviations for directed polymers in a random environment

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  • Carmona, Philippe
  • Hu, Yueyun

Abstract

For the model of directed polymers in a Gaussian random environment introduced by Imbrie and Spencer, we establish: - a Large Deviations Principle for the end position of the polymer under the Gibbs measure;- a scaling inequality between the volume exponent and the fluctuation exponent of the free energy;- a relationship between the volume exponent and the rate function of the Large Deviations Principle.

Suggested Citation

  • Carmona, Philippe & Hu, Yueyun, 2004. "Fluctuation exponents and large deviations for directed polymers in a random environment," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 285-308, August.
    • Handle: RePEc:eee:spapps:v:112:y:2004:i:2:p:285-308
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    Cited by:

    1. Liu, Quansheng & Watbled, Frédérique, 2009. "Exponential inequalities for martingales and asymptotic properties of the free energy of directed polymers in a random environment," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3101-3132, October.
    2. Francis Comets & Nobuo Yoshida, 2011. "Branching Random Walks in Space–Time Random Environment: Survival Probability, Global and Local Growth Rates," Journal of Theoretical Probability, Springer, vol. 24(3), pages 657-687, September.

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