The strict-weak lattice polymer

Abstract

We introduce the strict-weak polymer model, and show the KPZ universality of the free energy fluctuation of this model for a certain range of parameters. Our proof relies on the observation that the discrete time geometric q-TASEP model, studied earlier by A. Borodin and I. Corwin, scales to this polymer model in the limit q->1. This allows us to exploit the exact results for geometric q-TASEP to derive a Fredholm determinant formula for the strict-weak polymer, and in turn perform rigorous asymptotic analysis to show KPZ scaling and GUE Tracy-Widom limit for the free energy fluctuations. We also derive moments formulae for the polymer partition function directly by Bethe ansatz, and identify the limit of the free energy using a stationary version of the polymer model.

23 pages, 4 figures

References in corpus (2)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Log-Gamma directed polymer with fixed endpoints via the replica Bethe Ansatz

Cited by in corpus (2)

• Analytical Methods and Field Theory for Disordered Systems
• Crossover in the log-gamma polymer from the replica coordinate Bethe Ansatz