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

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  • Barraquand, Guillaume

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 Ferrari and Veto (2013) that the rescaled particles position of q-TASEP with identical hopping rates obeys a 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–Vető’s and does not require any condition on the parameter q nor the macroscopic position of particles.

Suggested Citation

  • Barraquand, Guillaume, 2015. "A phase transition for q-TASEP with a few slower particles," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2674-2699.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:7:p:2674-2699
    DOI: 10.1016/j.spa.2015.01.009
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    Cited by:

    1. Betea, D. & Ferrari, P.L. & Occelli, A., 2022. "The half-space Airy stat process," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 207-263.
    2. Lee, Eunghyun & Wang, Dong, 2019. "Distributions of a particle’s position and their asymptotics in the q-deformed totally asymmetric zero range process with site dependent jumping rates," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1795-1828.
    3. Vető, Bálint, 2022. "Asymptotic fluctuations of geometric q-TASEP, geometric q-PushTASEP and q-PushASEP," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 227-266.

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