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

125 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

Access to Document

10.1214/10-AOP632

Handle.net

Persistent link

Cite this

@article{04b31caa35e947ec8c44fc5aef448613,

title = "Directed polymers and the quantum Toda lattice",

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.",

keywords = "Random matrices, Whittaker functions",

author = "Neil O'Connell",

year = "2012",

month = mar,

doi = "10.1214/10-AOP632",

language = "English",

volume = "40",

pages = "437--458",

journal = "Annals of Probability",

issn = "0091-1798",

publisher = "Institute of Mathematical Studies",

number = "2",

}

TY - JOUR

T1 - Directed polymers and the quantum Toda lattice

AU - O'Connell, Neil

PY - 2012/3

Y1 - 2012/3

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=84860379569&partnerID=8YFLogxK

U2 - 10.1214/10-AOP632

DO - 10.1214/10-AOP632

M3 - Article (Academic Journal)

AN - SCOPUS:84860379569

SN - 0091-1798

VL - 40

SP - 437

EP - 458

JO - Annals of Probability

JF - Annals of Probability

IS - 2

ER -

Directed polymers and the quantum Toda lattice

Abstract

Keywords

Access to Document

Handle.net

Other files and links

Fingerprint

Cite this