Borodin–Péché Fluctuations of the Free Energy in Directed Random Polymer Models

Zsófia Talyigás, Bálint Vető

Research output: Contribution to journalArticlepeer-review

Abstract

We consider two directed polymer models in the Kardar–Parisi–Zhang (KPZ) universality class: the O’Connell–Yor semi-discrete directed polymer with boundary sources and the continuum directed random polymer with (m, n)-spiked boundary perturbations. The free energy of the continuum polymer is the Hopf–Cole solution of the KPZ equation with the corresponding (m, n)-spiked initial condition. This new initial condition is constructed using two semi-discrete polymer models with independent bulk randomness and coupled boundary sources. We prove that the limiting fluctuations of the free energies rescaled by the 1 / 3rd power of time in both polymer models converge to the Borodin–Péché-type deformations of the GUE Tracy–Widom distribution.

Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalJournal of Theoretical Probability
Volume2019
DOIs
Publication statusPublished - 23 May 2019

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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