Directed polymers and the quantum Toda lattice

Neil O'Connell*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

103 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 languageEnglish
Pages (from-to)437-458
Number of pages22
JournalAnnals of Probability
Volume40
Issue number2
DOIs
Publication statusPublished - Mar 2012

Keywords

  • Random matrices
  • Whittaker functions

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