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

Author

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  • Zsófia Talyigás

    (University of Bath)

  • Bálint Vető

    (Budapest University of Technology and Economics)

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.

Suggested Citation

  • Zsófia Talyigás & Bálint Vető, 2020. "Borodin–Péché Fluctuations of the Free Energy in Directed Random Polymer Models," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1426-1444, September.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:3:d:10.1007_s10959-019-00919-8
    DOI: 10.1007/s10959-019-00919-8
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