On the TASEP with second class particles

Eunghyun Lee

Published 2017-05-30Version 1

In this paper we study some conditional probabilities for the totally asymmetric simple exclusion processes (TASEP) with the second class particles. To be more specific, we consider a finite system with one first class particle and $N-1$ second class particles, and we assume that the first class particle is initially the leftmost particle and the initial positions of particles are arbitrary. For this initial condition, we find the probability that the first class particle is at $x$ and it is still the leftmost particle at time $t$. Also, we provide the formulas of these probabilities for some special initial configurations of the positions of the particles. In particular, we show that this probability with the step initial condition is expressed by the determinant of an $N\times N$ matrix of contour integrals.