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Tracy-Widom asymptotics for a random polymer model with gamma-distributed weights

Research output: Contribution to journalArticle

  • Neil O'Connell
  • Ortmann Janosch
Original languageEnglish
Article number25
Number of pages18
JournalElectronic Journal of Probability
Volume20
Early online date4 Jun 2015
DOIs
DateAccepted/In press - 6 Mar 2015
DateE-pub ahead of print - 4 Jun 2015
DatePublished (current) - 2015

Abstract

We establish Tracy-Widom asymptotics for the partition function of a random polymer model with gamma-distributed weights recently introduced by Seppalainen. We show that the partition function of this random polymer can be represented within the framework of the geometric RSK correspondence and consequently its law can be expressed in terms of Whittaker functions. This leads to a representation of the law of the partition function which is amenable to asymptotic analysis. In this model, the partition function plays a role analogous to the smallest eigenvalue in the Laguerre unitary ensemble of random matrix theory.

    Research areas

  • Geometric RSK correspondence, Polymer models, Whittaker functions

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