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

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