The Annals of Probability

Directed polymers and the quantum Toda lattice

Neil O’Connell

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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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Ann. Probab., Volume 40, Number 2 (2012), 437-458.

First available in Project Euclid: 26 March 2012

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Primary: 15A52 37K10: Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.) 60J65: Brownian motion [See also 58J65] 82D60: Polymers

Random matrices Whittaker functions


O’Connell, Neil. Directed polymers and the quantum Toda lattice. Ann. Probab. 40 (2012), no. 2, 437--458. doi:10.1214/10-AOP632.

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