非マルコフ完全非対称単純排他過程の流量の近似式 (可積分系数理の諸相)

Abstract

In this proceedings, first, two kinds of totally asymmetric simple exclusion process (TASEP) with periodic boundary condition (random and parallel updates versions) are explained. Explicit expressions of flow of the two models are shown with the derivation processes. Then, non-Markovian TASEP is introduced. Approximate expressions of flow is obtained by exploiting the expression of the parallel-update TASEP. Results of simulations agree well with the approximate expression. Discrepancy between the simulations and expression is explained by the effect of the third-order moment of waiting-time distribution when Gamma distribution is used. In Delayed-Exponential distribution case, no clear discrepancy is observed despite the approximation included in the expression.