交通流モデルに現れる超幾何級数解(理論,応用可積分系,<特集>平成18年研究部会連合発表会)

抄録

In the present paper, we investigate the asymmetric simple exclusion process with parallel dynamics on a ring of finite sites. We focus on the correspondence between the asymmetric exclusion process and the zero-range process, and exploit the recursion formula for the partition function of the zero-range process. Then, we find that the explicit formulas for the partition function and the average velocity (or the flux) in the steady state are expressed by the Gauss hypergeometric functions.