Distribution of a particle's position in the ASEP with the {alternating} initial condition

Details Distribution of a particle's position in the ASEP with the {alternating} initial condition Distribution of a particle's position in the ASEP with the {alternating} initial condition

2010-04-09

arxiv.org/abs/1004.1470v3

J Stat Phys (2010) 140: 635-647

Physics

Mathematical Physics

Version 3 expands the introduction and adds more references. Published version

Scientific paper

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

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