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

Guillaume Barraquand

doi:10.1016/j.spa.2015.01.009

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

Guillaume Barraquand

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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.

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Guillaume Barraquand. 2015-02-06. A phase transition for $q$-TASEP with a few slower particles. https://doi.org/10.1016/j.spa.2015.01.009

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