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Hoffmann-Jørgensen Inequalities for Random Walks on the Cone of Positive Definite Matrices

Author

Listed:
  • Armine Bagyan

    (Pennsylvania State University)

  • Donald Richards

    (Pennsylvania State University)

Abstract

We consider random walks on the cone of $$m \times m$$ m × m positive definite matrices, where the underlying random matrices have orthogonally invariant distributions on the cone and the Riemannian metric is the measure of distance on the cone. By applying results of Khare and Rajaratnam (Ann Probab 45:4101–4111, 2017), we obtain inequalities of Hoffmann-Jørgensen type for such random walks on the cone. In the case of the Wishart distribution $$W_m(a,I_m)$$ W m ( a , I m ) , with index parameter a and matrix parameter $$I_m$$ I m , the identity matrix, we derive explicit and computable bounds for each term appearing in the Hoffmann-Jørgensen inequalities.

Suggested Citation

  • Armine Bagyan & Donald Richards, 2023. "Hoffmann-Jørgensen Inequalities for Random Walks on the Cone of Positive Definite Matrices," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1181-1202, June.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:2:d:10.1007_s10959-022-01189-7
    DOI: 10.1007/s10959-022-01189-7
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    References listed on IDEAS

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