概率元胞自动机表示的粒子系统渐近分布的评价
Evaluation on asymptotic distribution of particle systems expressed by probabilistic cellular automata
摘要：
本文给出了概率Burgers元胞自动机（PBCA）的渐近分布的几种表示方法。PBCA由包含概率参数的简单粒子运动规则定义。渐近分布的配置收敛到一个唯一的PBCA的稳定状态。我们对该分布作了一些猜想，并导出了用GKZ超几何函数表示的渐近概率。如果我们把空间大小的极限取为无穷大，则可以计算无限大空间大小的粒子密度和通量之间的关系。此外，我们提出了两个扩展的PBCA系统，其渐近行为可以分析为PBCA。
英文摘要：
We propose some conjectures for asymptotic distribution of probabilistic Burgers cellular automaton (PBCA) which is defined by a simple motion rule of particles including a probabilistic parameter. Asymptotic distribution of configurations converges to a unique steady state for PBCA. We assume some conjecture on the distribution and derive the asymptotic probability expressed by GKZ hypergeometric function. If we take a limit of space size to infinity, a relation between density and flux of particles for infinite space size can be evaluated. Moreover, we propose two extended systems of PBCA of which asymptotic behavior can be analyzed as PBCA.
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