Tracy-Widom limit of q-Hahn TASEP

Abstract

We consider the q-Hahn TASEP which is a three-parameter family of discrete time interacting particle systems. The particles jump to the right independently according to a certain q-Binomial distribution with parallel updates. It is a generalization of the discrete time q-TASEP which is the q-deformed totally asymmetric simple exclusion process (TASEP) on Z for q in [0,1). For step initial condition, we prove that the current fluctuation of q-Hahn TASEP at time t is of order $t^{1/3}$ and asymptotically distributed as the GUE Tracy-Widom distribution. We verify the KPZ scaling theory conjecture for the q-Hahn TASEP.

23 pages, 3 figures

References in corpus (8)

• Fluctuation properties of the TASEP with periodic initial configuration
• Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition
• From interacting particle systems to random matrices
• Spectral theory for interacting particle systems solvable by coordinate Bethe ansatz
• A phase transition for $q$-TASEP with a few slower particles
• The $q$-Hahn asymmetric exclusion process
• A short proof of a symmetry identity for the $(q,\mu ,\nu )$-deformed Binomial distribution
• Enhanced Binding in Quantum Field Theory

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• Nonstationary generalized TASEP in KPZ and jamming regimes
• Parameter Permutation Symmetry in Particle Systems and Random Polymers
• Asymptotic fluctuations of geometric q-TASEP, geometric q-PushTASEP and q-PushASEP
• Stochastic Baxterisation of a fused Hecke algebra