This talk will focus on the study of large deviations of the free energy in the O’Connell-Yor polymer, which is an exactly solvable 1+1 dimensional directed polymer model. This question is equivalent to the study of Lyapunov exponents for the partition function, which solves a parabolic stochastic partial differential equation (SPDE) that can be viewed as a “totally asymmetric” version of the one dimensional semi-discrete (space discrete, time continuous) stochastic heat equation. Lyapunov exponents for parabolic SPDEs are often studied in connection with the physical phenomenon of intermittency.
The main result to be discussed is an explicit computation of all positive Lyapunov exponents and, equivalently, the computation of the rate n large deviation rate function for the normalized free energy density in the polymer mode