The Annals of Probability
- Ann. Probab.
- Volume 40, Number 2 (2012), 437-458.
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.
Ann. Probab., Volume 40, Number 2 (2012), 437-458.
First available in Project Euclid: 26 March 2012
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O’Connell, Neil. Directed polymers and the quantum Toda lattice. Ann. Probab. 40 (2012), no. 2, 437--458. doi:10.1214/10-AOP632. https://projecteuclid.org/euclid.aop/1332772711