论文标题
随机几何图的长度功率功能的协方差矩阵 - 渐近分析
Covariance matrices of length power functionals of random geometric graphs -- an asymptotic analysis
论文作者
论文摘要
研究了随机几何图的长度功率功能的矢量的渐近特性。更确切地说，随着潜在均匀泊松点的强度增加，它的渐近协方差矩阵进行了研究。这包括对矩阵属性等级别，确定性，决定因素，特征空间或感兴趣的分解的系统讨论。对于结果的表述，有必要区分。确实，在这三个可能的制度中，各个协方差矩阵具有完全不同的性质，导致不同的陈述。最后，得出了随机几何图的随机后果。
Asymptotic properties of a vector of length power functionals of random geometric graphs are investigated. More precisely, its asymptotic covariance matrix is studied as the intensity of the underlying homogeneous Poisson point process increases. This includes a systematic discussion of matrix properties like rank, definiteness, determinant, eigenspaces or decompositions of interest. For the formulation of the results a case distinction is necessary. Indeed, in the three possible regimes the respective covariance matrix is of quite different nature which leads to different statements. Finally, stochastic consequences for random geometric graphs are derived.
