有界区域上的二维随机游动
Two-dimensional random walk in a bounded domain
摘要：
在最近的一封信中，Ciftci和Cakmak [EPL 87，60003（2009）]表明，有界域中的二维随机行走，其中穿过边界的行走者返回到原点附近的基弧，具有确定性规则，可以产生规则模式。我们的数值计算表明，返回的步行者沿着基曲线的累积概率分布函数是魔鬼的楼梯，这可以解释从这些步行映射到一个非线性随机映射。非平凡概率分布函数（PDF）是CCRW的一个普遍特征，其特征在于PDF边界曲线的分形维数d=1.75（0）。
英文摘要：
In a recent Letter Ciftci and Cakmak [EPL 87, 60003 (2009)] showed that the two dimensional random walk in a bounded domain, where walkers which cross the boundary return to a base curve near origin with deterministic rules, can produce regular patterns. Our numerical calculations suggest that the cumulative probability distribution function of the returning walkers along the base curve is a Devil's staircase, which can be explained from the mapping of these walks to a non-linear stochastic map. The non-trivial probability distribution function(PDF) is a universal feature of CCRW characterized by the fractal dimension d=1.75(0) of the PDF bounding curve.
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