2014/09/30 by Ivan Corwin, Timo Seppäläinen, Hao Shen · 2 citations
Materials Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Combinatorics #Condensed matter physics #Dendrimers and Hyperbranched Polymers #Lattice (music) #Mathematics #Physics #Polymer #Random Matrices and Applications #Statistical physics #cond-mat.stat-mech #math-ph #math.MP #math.PR
paper · pdf · doi:10.1007/s10955-015-1267-0
23 pages, 4 figures
openalex publication_date 2015/04/30 · arxiv created 2015/07/06 · arxiv updated 2015/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.