The strict-weak lattice polymer. (English) Zbl 1323.82059
Summary: 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 [Int. Math. Res. Not. 2015, No. 2, 499–537 (2015; Zbl 1310.82030)], scales to this polymer model in the limit \(q\to 1\). 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.
MSC:
| 82D60 | Statistical mechanics of polymers |
| 82C20 | Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics |
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
| 82C23 | Exactly solvable dynamic models in time-dependent statistical mechanics |
| 44A10 | Laplace transform |
Keywords:
directed polymer; Fredholm determinant; Kardar-Parisi-Zhang; \(q\)-TASEP; replica method; Tracy-Widom distributionCitations:
Zbl 1310.82030References:
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