Directed polymers and the quantum Toda lattice

Neil O'Connell

doi:10.1214/10-AOP632

Directed polymers and the quantum Toda lattice

Neil O'Connell^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

129 Citations (Scopus)

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.

Original language	English
Pages (from-to)	437-458
Number of pages	22
Journal	Annals of Probability
Volume	40
Issue number	2
DOIs	https://doi.org/10.1214/10-AOP632
Publication status	Published - Mar 2012

Keywords

Random matrices
Whittaker functions

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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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AB - 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.

KW - Random matrices

KW - Whittaker functions

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DO - 10.1214/10-AOP632

M3 - Article (Academic Journal)

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SP - 437

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JO - Annals of Probability

JF - Annals of Probability

IS - 2

ER -

Directed polymers and the quantum Toda lattice

Abstract

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