The strict-weak lattice polymer

TL;DR

This paper introduces the strict-weak polymer model, demonstrating its KPZ universality for free energy fluctuations by connecting it to geometric q-TASEP and employing exact formulas and asymptotic analysis.

Contribution

The paper establishes the KPZ universality of the strict-weak polymer model and derives exact formulas using Bethe ansatz and scaling limits from q-TASEP.

Findings

Proves KPZ scaling and GUE Tracy-Widom limit for free energy fluctuations.

Derives exact moments formulas via Bethe ansatz.

Connects the polymer model to geometric q-TASEP in the limit q->1.

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.