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

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  • Gnacadja, Gilles
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    Abstract

    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

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 10 ()
    Pages: 1849-1852

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:10:p:1849-1852

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    Related research

    Keywords: Equidistribution; Congruence classes in probability convolution; Circulant matrix; Doubly stochastic matrix; Inventory replenishment;

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