Directed polymers and the quantum Toda lattice

Neil O'Connell
2012 Annals of Probability  
We characterize the law of the partition function of a Brownian directed polymer model in terms of a diffusion process associated with the quantum Toda lattice. The proof is via a multidimensional generalization of a theorem of Matsumoto and Yor concerning exponential functionals of Brownian motion. It is based on a mapping which can be regarded as a geometric variant of the RSK correspondence.
doi:10.1214/10-aop632 fatcat:ckz3d2xlxfhnpmsljtzo4xolwq