空间随机划分过程的组合分析和近似分析
Combinatorial and approximative analyses in a spatially random division process
摘要：
对于空间特性，玻璃破碎块度、玻璃质量、城市道路围合面积和散堆填料孔径/体积的频率分布普遍存在厚尾现象。为了给一个新的分析方法的分布，我们考虑了一个简单的模型，它构造了一个分形的分层网络的基础上随机划分的矩形。随机过程构成一个马尔可夫链，对应于分裂成四个粒子的定向随机游动。我们推导了矩形面积分布的组合解析形式及其连续近似，并在数值上显示了与实际分布的良好拟合。
英文摘要：
For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for the distributions, we consider a simple model which constructs a fractal-like hierarchical network based on random divisions of rectangles. The stochastic process makes a Markov chain and corresponds to directional random walks with splitting into four particles. We derive a combinatorial analytical form and its continuous approximation for the distribution of rectangle areas, and numerically show a good fitting with the actual distribution in the averaging behavior of the divisions.
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