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Directed polymers and the quantum Toda lattice

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.

preprint2012arXivOpen access
Neil O'Connell
math-phmath.PRmath.MP
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Neil O'Connell

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