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arXiv · 1004.1470

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

Eunghyun Lee
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Abstract

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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Eunghyun Lee. 2010-04-09. Distribution of a particle's position in the ASEP with the {alternating} initial condition. https://doi.org/10.1007/s10955-010-0014-9

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