Directed polymers and the quantum Toda lattice

Neil O'Connell*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

94 Citations (Scopus)


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
Issue number2
Publication statusPublished - Mar 2012


  • Random matrices
  • Whittaker functions


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