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 (10)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Scaling for a one-dimensional directed polymer with boundary conditions
• Directed polymers and the quantum Toda lattice
• Log-Gamma polymer free energy fluctuations via a Fredholm determinant identity
• Random-walk in Beta-distributed random environment
• Tropical Combinatorics and Whittaker functions
• Spectral theory for the q-Boson particle system
• Spectral theory for interacting particle systems solvable by coordinate Bethe ansatz
• Height fluctuations for the stationary KPZ equation
• Log-Gamma directed polymer with fixed endpoints via the replica Bethe Ansatz

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• Exact solution for a random walk in a time-dependent 1D random environment: the point-to-point Beta polymer
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• Large deviations for some corner growth models with inhomogeneity
• Intermediate disorder directed polymers and the multi-layer extension of the stochastic heat equation
• Observables of coloured stochastic vertex models and their polymer limits
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• Scaling limits for non-intersecting polymers and Whittaker measures
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• Midpoint distribution of directed polymers in the stationary regime: exact result through linear response
• Hidden diagonal integrability of $q$-Hahn vertex model and Beta polymer model
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• Log-gamma directed polymer with one free end via coordinate Bethe Ansatz
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• Borodin-Péché fluctuations of the free energy in directed random polymer models
• Matrix Whittaker processes
• Localization length of the $1+1$ continuum directed random polymer
• Analytical Methods and Field Theory for Disordered Systems
• On the stationary solutions of random polymer models and their zero-temperature limits
• Localization and free energy asymptotics in disordered statistical mechanics and random growth models
• Crossover in the log-gamma polymer from the replica coordinate Bethe Ansatz