Distribution of a Particle’s Position in the ASEP with the Alternating Initial Condition

摘要

In this paper we give the distribution of the position of a particle in the asymmetric simple exclusion process (ASEP) with the alternating initial condition. That is, we find ℙ(X _m (t)≤x) where X _m (t) is the position of the particle at time t which was at m=2k−1, k∈ℤ at t=0. As in the ASEP with step initial condition, there arises a new combinatorial identity for the alternating initial condition, and this identity relates the integrand of the integral formula for ℙ(X _m (t)≤x) to a determinantal form together with an extra product.