含有少量慢粒子的$q$ - TASEP体系的相变
A phase transition for $q$-TASEP with a few slower particles
摘要：
考虑了一个从阶跃初始条件出发的$q$ -TASEP模型，其中除了极少数粒子外，其余粒子都有速度$1$，少数粒子速度较慢.文献[9]证明了具有相同跳频率的$q$ -TASEP的重标度粒子位置服从Tracy-Widom的中心极限定理.我们适应这项工作的情况下，不同的跳跃率，并表明，观察到所谓的BBP过渡。我们的证明是一个改进的Ferrari-Vetö的，不需要任何条件的参数$q$，也没有宏观位置的粒子。
英文摘要：
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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