Large deviations of the free energy in the O'Connell-Yor polymer

TL;DR

This paper studies the rare fluctuations of the free energy in the O'Connell-Yor polymer model using advanced probabilistic techniques, providing exact formulas and dual representations for large deviation behaviors.

Contribution

It introduces a novel variational approach to compute all real moment Lyapunov exponents and derives a dual form of the large deviation rate function for the model.

Findings

Exact formulas for all real moment Lyapunov exponents.

Dual representation of the large deviation rate function.

Method applicable to related stochastic models.

Abstract

We investigate large deviations of the free energy in the O'Connell-Yor polymer through a variational representation of the positive real moment Lyapunov exponents of the associated parabolic Anderson model. Our methods yield an exact formula for all real moment Lyapunov exponents of the parabolic Anderson model and a dual representation of the large deviation rate function with normalization $n$ for the free energy.