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The Poisson Distribution for Linear Statistics of Random Permutations

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Abstract

We examine the asymptotic distribution laws of integer-valued linear statistics defined via the multiplicities of lengths of cycles comprising a random permutation taken with equal probability. We establish necessary and sufficient conditions for the weak convergence to the Poisson limit law. The approach can be applied to investigate other logarithmic structures.

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Authors and Affiliations

  1. Vilnius University, Naugarduko 24, LT-03225, Vilnius, Lithuania

    E. Manstavicius

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  1. E. Manstavicius
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Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 537–552, October–December, 2005.

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Manstavicius, E. The Poisson Distribution for Linear Statistics of Random Permutations. Lith Math J 45, 434–446 (2005). https://doi.org/10.1007/s10986-006-0006-2

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  • DOI: https://doi.org/10.1007/s10986-006-0006-2

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