论文标题
Wigner和WishArt合奏用于图形模型
Wigner and Wishart Ensembles for graphical models
论文作者
论文摘要
Vinberg锥和环境矢量空间在稀疏模型和图形模型的现代统计中很重要。本文的目的是研究与不断增长的Vinberg矩阵有关的高斯，Wigner和协方差矩阵的特征值分布，对应于日益增长的雏菊图。对于高斯或Wigner合奏，我们为限制分布提供了明确的公式。对于Vinberg锥上自然定义的WishArt合奏，其限制性stieltjes变换，在0处的支持和原子在0中用Lambert-Tsallis功能明确描述，这些功能是通过使用Tsallis $ q $ uppartential功能来定义的。
Vinberg cones and the ambient vector spaces are important in modern statistics of sparse models and of graphical models. The aim of this paper is to study eigenvalue distributions of Gaussian, Wigner and covariance matrices related to growing Vinberg matrices, corresponding to growing daisy graphs. For Gaussian or Wigner ensembles, we give an explicit formula for the limiting distribution. For Wishart ensembles defined naturally on Vinberg cones, their limiting Stieltjes transforms, support and atom at 0 are described explicitly in terms of the Lambert-Tsallis functions, which are defined by using the Tsallis $q$-exponential functions.
