A phase transition for $q$-TASEP with a few slower particles

Abstract

We consider a $q$-TASEP model started from step initial condition where all but finitely many particles have speed $1$ and a few particles are slower. It is shown in [9] that the rescaled particles position of $q$-TASEP with identical hopping rates obeys a central limit theorem à la Tracy-Widom. We adapt this work to the case of different hopping rates and show that one observes the so-called BBP transition. Our proof is a refinement of Ferrari-Vetö's and does not require any condition on the parameter $q$ nor the macroscopic position of particles.

arXiv comment27 pages, 5 figures

References in corpus (4)

• Shape Fluctuations and Random Matrices
• Directed polymers and the quantum Toda lattice
• From duality to determinants for q-TASEP and ASEP
• KPZ Scaling Theory and the Semi-discrete Directed Polymer Model

Cited by in corpus (24)

• Random-walk in Beta-distributed random environment
• Half-space Macdonald processes
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• Transversal fluctuations of the ASEP, stochastic six vertex model, and Hall-Littlewood Gibbsian line ensembles
• Generalizations of TASEP in discrete and continuous inhomogeneous space
• The $q$-Hahn asymmetric exclusion process
• Stationary half-space last passage percolation
• Height fluctuations for the stationary KPZ equation
• Fluctuations of the log-gamma polymer free energy with general parameters and slopes
• The KPZ equation in a half space with flat initial condition and the unbinding of a directed polymer from an attractive wall
• Hall-Littlewood-PushTASEP and its KPZ limit
• Tracy-Widom limit of q-Hahn TASEP
• Fluctuations for stationary $q$-TASEP
• Free field theory and observables of periodic Macdonald processes
• Tracy-Widom asymptotics for a river delta model
• Stationary Higher Spin Six Vertex Model and $q$-Whittaker measure
• Distributions of a particle's position and their asymptotics in the $q$-deformed totally asymmetric zero range process with site dependent jumping rates
• Asymptotics of free fermions in a quadratic well at finite temperature and the Moshe-Neuberger-Shapiro random matrix model
• Q-zero range has random walking shocks
• Nonstationary generalized TASEP in KPZ and jamming regimes
• Free field approach to the Macdonald process
• Asymptotic fluctuations of geometric q-TASEP, geometric q-PushTASEP and q-PushASEP
• The half-space Airy stat process
• The q-Hahn PushTASEP