Betti numbers of random manifolds
Betti numbers of random manifolds
复制标题
随机流形的贝蒂数
DOI：
--
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
T. Kappeler
中科院分区：
文献类型：
--
作者：
M. Farber;T. Kappeler
机械连杆配置空间（也称为多边形空间）的贝蒂数取决于大量参数——连杆杆的长度。受拓扑机器人学、统计形状理论和分子生物学应用的推动，我们将这些长度视为随机变量，并研究当链接数 n 趋于无穷大时平均 Betti 数的渐近值。我们建立了一个令人惊讶的事实，即对于相当充足的概率测度序列类别，平均贝蒂数的渐近值与测度的选择无关。本文的主要结果适用于平面连杆以及 R3 中的连杆。我们还证明了贝蒂数更高矩的结果。 （© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA，魏因海姆）
Betti numbers of configuration spaces of mechanical linkages (known also as polygon spaces) depend on a large number of parameters – the lengths of the bars of the linkage. Motivated by applications in topological robotics, statistical shape theory and molecular biology, we view these lengths as random variables and study asymptotic values of the average Betti numbers as the number of links n tends to infinity. We establish a surprising fact that for a reasonably ample class of sequences of probability measures the asymptotic values of the average Betti numbers are independent of the choice of the measure. The main results of the paper apply to planar linkages as well as for linkages in R3. We also prove results about higher moments of Betti numbers. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)