人口分布的有限尺寸标度及其与分形空间结构的关系
Finite-size scaling of human-population distributions over fixed-size cells and its relation to fractal spatial structure
摘要：
使用高空间分辨率的人口数据，在欧洲南部的一个地区，我们研究人口在固定大小的空间单元。我们发现，与直觉相反，每个细胞的居民数量的分布增加其可变性时，细胞的大小增加。然而，分布的形状保持不变，这使我们能够引入一个标度律，类似于有限尺寸标度，标度函数与伽马分布相当好地拟合。这意味着每个小区的居民数量的分布是稳定的或不变的下添加与相邻小区（加上重新缩放），无视中心极限定理，由于随机变量的明显依赖性。有限尺寸标度意味着分布的矩与其尺度参数之间存在幂律关系，这与种群形成的空间格局的分形性质有关。理论预测和经验结果之间的匹配相当不错。
英文摘要：
Using demographic data of high spatial resolution for a region in the south of Europe, we study the population over fixed-size spatial cells. We find that, counterintuitively, the distribution of the number of inhabitants per cell increases its variability when the size of the cells is increased. Nevertheless, the shape of the distributions is kept constant, which allows us to introduce a scaling law, analogous to finite-size scaling, with a scaling function reasonably well fitted by a gamma distribution. This means that the distribution of the number of inhabitants per cell is stable or invariant under addition with neighboring cells (plus rescaling), defying the central-limit theorem, due to the obvious dependence of the random variables. The finite-size scaling implies a power-law relations between the moments of the distribution and its scale parameter, which are found to be related with the fractal properties of the spatial pattern formed by the population. The match between theoretical predictions and empirical results is reasonably good.
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