Thursday, March 29, 2012

0910.0069 (Neil O'Connell)

Directed polymers and the quantum Toda lattice    [PDF]

Neil O'Connell
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.
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