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

Zsófia Talyigás () and Bálint Vető ()
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Zsófia Talyigás: University of Bath
Bálint Vető: Budapest University of Technology and Economics

Journal of Theoretical Probability, 2020, vol. 33, issue 3, 1426-1444

Abstract: 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.

Date: 2020
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DOI: 10.1007/s10959-019-00919-8

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