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Asymptotic equidistribution of congruence classes with respect to the convolution iterates of a probability vector


  • Gnacadja, Gilles


Consider a positive integer d and a positive probability vector f over the numbers 0,…,ℓ. The n-fold convolution f∗n of f is a probability vector over the numbers 0,…,nℓ, and these can be partitioned into congruence classes modulo d. The main result of this paper is that, asymptotically in n, these d congruence classes have equiprobability 1/d. In the motivating application, one has N containers of capacity d and repeatedly retrieves one item from each of M randomly selected containers (0

Suggested Citation

  • Gnacadja, Gilles, 2012. "Asymptotic equidistribution of congruence classes with respect to the convolution iterates of a probability vector," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1849-1852.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:10:p:1849-1852
    DOI: 10.1016/j.spl.2012.05.025

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    Cited by:

    1. Bolaños-Servin, Jorge R. & Carbone, Raffaella & Quezada, Roberto, 2017. "On reducibility and spectral properties of circulant Markov processes," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 27-33.


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