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Wigner and Wishart Ensembles for graphical models

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. Eigenvalue distributions and graphical models and covariance matrices and Wigner matrices and homogeneous cones and Vinberg cones and q-exponential and Lambert-Tsallis functions
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https://hal.archives-ouvertes.fr/hal-02926753
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Submitted on : Tuesday, September 1, 2020 - 8:29:08 AM
Last modification on : Thursday, September 3, 2020 - 4:50:05 AM
Long-term archiving on: : Wednesday, December 2, 2020 - 12:57:56 PM

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Hideto Nakashima, Piotr Graczyk. Wigner and Wishart Ensembles for graphical models. 2020. ⟨hal-02926753⟩

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