Some conditional probabilities in the TASEP with second class particles

Abstract

In this paper we consider the TASEP with second class particles with the initial order is such that $k$ first class particles are located to the left of $N-k$ second class particles. Under this assumption of the initial state of order, we find the probability that the first class particles are at $x,x+1,\cdots ,x+k-1$ and the first class particles are still located to the left of all second class particles at later time $t$. Moreover, we obtain an explicit formula of this probability for the step initial condition. This probability generalizes a result for $k=1$ in Lee (arXiv:1705.10544).

Published version

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Cited by in corpus (1)

• Distribution of a second-class particle's position in the two-species ASEP with a special initial configuration