Scaling limits for non-intersecting polymers and Whittaker measures

Samuel Johnston, Neil O'Connell

Research output: Contribution to journalArticlepeer-review

3 Citations (SciVal)

Abstract

We study the partition functions associated with non-intersecting polymers in a random environment. By considering paths in series and in parallel, the partition functions carry natural notions of subadditivity, allowing the effective study of their asymptotics. For a certain choice of random environment, the geometric RSK correspondence provides an explicit representation of the partition functions in terms of a stochastic interface. Formally this leads to a variational description of the macroscopic behaviour of the interface and hence the free energy of the associated non-intersecting polymer model. At zero temperature we relate this variational description to the Marčenko–Pastur distribution, and give a new derivation of the surface tension of the bead model.
Original languageEnglish
Pages (from-to)354–407
JournalJournal of Statistical Physics
Volume179
DOIs
Publication statusPublished - 2 Oct 2020

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