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

Gilles Gnacadja

Statistics & Probability Letters, 2012, vol. 82, issue 10, 1849-1852

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 (0Keywords: Equidistribution; Congruence classes in probability convolution; Circulant matrix; Doubly stochastic matrix; Inventory replenishment (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spl.2012.05.025

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