On the Free Energy of a Directed Polymer in a Brownian Environment

#### J. Moriarty, N. O'Connell

2007, v.13, Issue 2, 251-266

ABSTRACT

We prove a formula conjectured in [N. O'Connell and M. Yor, Brownian analogues of Burke's theorem, Stoch. Process. Appl., 2001, v. 96, N 2, 285-304] for the free energy density of a directed polymer in a Brownian environment in $1+1$ dimensions.

Keywords: directed polymers,exponential functionals of Brownianmotion,quasi-reversibility,Brownian queues,large deviations