Tracy-Widom asymptotics for q-TASEP

Abstract

We consider the q-TASEP that is a q-deformation of the totally asymmetric simple exclusion process (TASEP) on Z for q in [0,1) where the jump rates depend on the gap to the next particle. For step initial condition, we prove that the current fluctuation of q-TASEP at time t are of order t^{1/3} and asymptotically distributed as the GUE Tracy-Widom distribution, which confirms the KPZ scaling theory conjecture.

24 pages, 5 figures

References in corpus (7)

• Fluctuation properties of the TASEP with periodic initial configuration
• From duality to determinants for q-TASEP and ASEP
• Spectral theory for the q-Boson particle system
• Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition
• From interacting particle systems to random matrices
• A phase transition for $q$-TASEP with a few slower particles
• The transition probability and the probability for the left-most particle's position of the q-TAZRP

Cited by in corpus (15)

• Stochastic six-vertex model
• Random-walk in Beta-distributed random environment
• A Pfaffian representation for flat ASEP
• Half-space Macdonald processes
• Transversal fluctuations of the ASEP, stochastic six vertex model, and Hall-Littlewood Gibbsian line ensembles
• The $q$-Hahn asymmetric exclusion process
• Determinantal structures in the O'Connell-Yor directed random polymer model
• Stationary half-space last passage percolation
• Hidden diagonal integrability of $q$-Hahn vertex model and Beta polymer model
• Free field theory and observables of periodic Macdonald processes
• Tracy-Widom asymptotics for a river delta model
• Current statistics in the q-boson zero range process
• Q-zero range has random walking shocks
• TASEP with a general initial condition and a deterministically moving wall
• Asymptotic fluctuations of geometric q-TASEP, geometric q-PushTASEP and q-PushASEP