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A characterization of the type of the Cauchy-Hua measure on real symmetric matrices

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Abstract

The Cauchy-Hua measure is the probability on the set ofn×n real symmetric matrices of densitys ↦ C n/det(I + s 2)(n + 1)/2 . For any probability measure μ on the set ofn×n real symmetric matrices, we define (if μ verifies an additional condition) the image of μ by a 2n×2n real symplectic matrix, and we introduce the type of μ. Then, the type of the Cauchy-Hua measure is characterized from its invariance by the symplectic group.

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Authors and Affiliations

  1. Laboratoire de Statistique et Probabilités, U.A.-C.N.R.S. No. 745 Université Paul Sabatier, Toulouse, France

    Jean-Louis Dunau & Henri Senateur

  2. Institut National des Sciences Appliquées, Toulouse

    Jean-Louis Dunau

Authors
  1. Jean-Louis Dunau
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  2. Henri Senateur
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Dunau, JL., Senateur, H. A characterization of the type of the Cauchy-Hua measure on real symmetric matrices. J Theor Probab 1, 263–270 (1988). https://doi.org/10.1007/BF01246629

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  • DOI: https://doi.org/10.1007/BF01246629

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