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arXiv · 0910.0069

Directed polymers and the quantum Toda lattice

Neil O'Connell
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Abstract

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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Neil O'Connell. 2009-10-01. Directed polymers and the quantum Toda lattice. https://doi.org/10.1214/10-aop632

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