Experiments Suggesting That the Distribution of the Hyperbolic Length of Closed Geodesics Sampling by Word Length Is Gaussian
Experiments Suggesting That the Distribution of the Hyperbolic Length of Closed Geodesics Sampling by Word Length Is Gaussian
复制标题
字长闭合测地线采样双曲长度服从高斯分布的实验
作者：
Moira Chas;Keren Li;B. Maskit
有边界曲面上的有向闭曲线的每一个自由同伦类都可以用基群及其逆的生成子中的一个循环约简字来描述。单词长度是循环单词的字母数。如果曲面具有带测地线边界的双曲度规，则该类的几何长度为该类中唯一测地线的长度。通过计算机实验，我们研究了裤子表面上具有给定单词长度的所有类之间的几何长度分布。我们的实验有力地表明，分布是正态的。
Each free homotopy class of directed closed curves on a surface with boundary can be described by a cyclic reduced word in the generators of the fundamental group and their inverses. The word length is the number of letters of the cyclic word. If the surface has a hyperbolic metric with geodesic boundary, the geometric length of the class is the length of the unique geodesic in that class. By computer experiments, we investigate the distribution of the geometric length among all classes with a given word length on the pair of pants surface. Our experiments strongly suggest that the distribution is normal.