Borodin-P\'ech\'e fluctuations of the free energy in directed random polymer models
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.
Keywords
Cite
@article{arxiv.1809.09869,
title = {Borodin-P\'ech\'e fluctuations of the free energy in directed random polymer models},
author = {Zsófia Talyigás and Bálint Vető},
journal= {arXiv preprint arXiv:1809.09869},
year = {2020}
}
Comments
15 pages, 4 figures