Directed polymers and the quantum Toda lattice [PDF]
Neil O'ConnellWe 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.View original: http://arxiv.org/abs/0910.0069
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