Self-intersections in combinatorial topology: statistical structure
Self-intersections in combinatorial topology: statistical structure
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组合拓扑中的自交：统计结构
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
S. Lalley
中科院分区：
文献类型：
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作者：
Moira Chas;S. Lalley
用基本群及其逆的生成元中的约化循环词来刻画有向边界可定向曲面上的定向闭合曲线，直至连续变形。所谓自交，1是指类的代表的横截自交点的最小个数。我们证明了如果从m个字母的所有类别中随机选择一个类别，则对于较大的m，其自交数的分布接近于高斯分布。这一定理是由一项计算机实验得出的，该实验有400万条曲线，其分布非常接近于高斯分布。
Oriented closed curves on an orientable surface with boundary are described up to continuous deformation by reduced cyclic words in the generators of the fundamental group and their inverses. By self-intersection number one means the minimum number of transversal self-intersection points of representatives of the class. We prove that if a class is chosen at random from among all classes of m letters, then for large m the distribution of the self-intersection number approaches the Gaussian distribution. The theorem was strongly suggested by a computer experiment with four million curves producing a very nearly Gaussian distribution.