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arXiv · 1809.09869

Borodin-Péché fluctuations of the free energy in directed random polymer models

Zsófia Talyigás·Bálint Vető
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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-Peche type deformations of the GUE Tracy-Widom distribution.

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Zsófia Talyigás, Bálint Vető. 2019-05-17. Borodin-Péché fluctuations of the free energy in directed random polymer models. https://doi.org/10.1007/s10959-019-00919-8

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