Wigner and Wishart Ensembles for graphical models

DOI10.1007/S10463-021-00800-8arXiv2008.10446MaRDI QIDQ6347620

Publication date: 10 August 2020

Abstract: 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.

Mathematics Subject Classification ID

Statistics (62-XX)

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