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Entropy and Convergence on Compact Groups

Author

Listed:
  • Oliver Johnson

    (CMS)

  • Yurii Suhov

    (CMS
    Institute for Problems of Information Transmission)

Abstract

We investigate the behaviour of the entropy of convolutions of independent random variables on compact groups. We provide an explicit exponential bound on the rate of convergence of entropy to its maximum. Equivalently, this proves convergence of the density to uniformity, in the sense of Kullback–Leibler. We prove that this convergence lies strictly between uniform convergence of densities (as investigated by Shlosman and Major), and weak convergence (the sense of the classical Ito–Kawada theorem). In fact it lies between convergence in L 1+ε and convergence in L 1.

Suggested Citation

  • Oliver Johnson & Yurii Suhov, 2000. "Entropy and Convergence on Compact Groups," Journal of Theoretical Probability, Springer, vol. 13(3), pages 843-857, July.
    • Handle: RePEc:spr:jotpro:v:13:y:2000:i:3:d:10.1023_a:1007818830500
    DOI: 10.1023/A:1007818830500
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