Asymptotic Normality in the Classical Ball Problem

Sevast'yanov, Boris Alexandrovich; Chistyakov, V. P.

doi:10.1137/1109034

Cited by 42 publications

(13 citation statements)

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“…A similar asymptotic behaviour has the number of cells with r-tuple occupancy (B6k6ssy [1]). The main multivariate theorem of the theory has been shown by Sevast'janov and Cist'jakov [6] (see also Koldin et al [2]) on the basis of R6nyi's paper [5]. Here we show that the result may be improved from the multivariate local limit theorem.…”

Section: A New Proof Of Generalized Theorem Of Irving Weiss I Kopocisupporting

confidence: 58%

A new proof of generalized theorem of Irving Weiss

Kopocińska

Kopociński

1992

Period Math Hung

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Section: A New Proof Of Generalized Theorem Of Irving Weiss I Kopocisupporting

confidence: 58%

A new proof of generalized theorem of Irving Weiss

Kopocińska

Kopociński

1992

Period Math Hung

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“…To derive the independence assumption, we could try a model based on Markov chains on urns. Indeed, an alternative proof of (6), can be obtained by using an urn model, as in Sevastyanov and Chistyakov, [39] and Chistyakov, [8], the Poissonization method and the standard saddle-point method (see, for instance, Flajolet and Sedgewick [16]). This will be the object of future work.…”

Section: Some Perspectivementioning

confidence: 99%

Distinctness of compositions of an integer: A probabilistic analysis

Hitczenko

Louchard

2001

Random Struct Algorithms

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ABSTRACT:Compositions of integers are used as theoretical models for many applications.The degree of distinctness of a composition is a natural and important parameter. In this article, we use as measure of distinctness the number of distinct parts (or components). We investigate, from a probabilistic point of view, the first empty part, the maximum part size and the distribution of the number of distinct part sizes. We obtain asymptotically, for the classical composition of an integer, the moments and an expression for a continuous distribution F, the (discrete) distribution of the number of distinct part sizes being computable from F. We next analyze another composition: the Carlitz one, where two successive parts are different. We use tools such as analytical depoissonization, Mellin transforms, Markov chain potential theory, limiting hitting times, singularity analysis and perturbation analysis.

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“…Proof. For n = 2,3,..., we introduce the events .. = 0, the probabilities (1.2) concerning the colouring are fixed and the condition n/N -> c> 0 holds as n -> oo, then an asymptotic estimate for the probability π^*) can be derived by the use of results from [8,9], if we take into account that by virtue of (2.6) the probability ττ^ can be rewritten as where the contour C goes around the point ζ = 0.…”

Section: Some Properties Of the Probability 7tmentioning

confidence: 99%