Open Access
Translator Disclaimer
March 2012 Directed polymers and the quantum Toda lattice
Neil O’Connell
Ann. Probab. 40(2): 437-458 (March 2012). DOI: 10.1214/10-AOP632

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.

Citation

Download Citation

Neil O’Connell. "Directed polymers and the quantum Toda lattice." Ann. Probab. 40 (2) 437 - 458, March 2012. https://doi.org/10.1214/10-AOP632

Information

Published: March 2012
First available in Project Euclid: 26 March 2012

zbMATH: 1245.82091
MathSciNet: MR2952082
Digital Object Identifier: 10.1214/10-AOP632

Subjects:
Primary: 15A52 , 37K10 , 60J65 , 82D60

Keywords: random matrices , Whittaker functions

Rights: Copyright © 2012 Institute of Mathematical Statistics

JOURNAL ARTICLE
22 PAGES


SHARE
Vol.40 • No. 2 • March 2012
Back to Top