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On Statistics of Permutations Chosen From the Ewens Distribution

Published online by Cambridge University Press:  22 August 2014

TATJANA BAKSHAJEVA  and
EUGENIJUS MANSTAVIČIUS
TATJANA BAKSHAJEVA
Affiliation:
Faculty of Mathematics and Informatics, Vilnius University, Naugarduko str. 24, LT-03225 Vilnius, Lithuania (e-mail: tania.kargina@gmail.com)
EUGENIJUS MANSTAVIČIUS
Affiliation:
Institute of Mathematics and Informatics, Vilnius University, Akademijos 4, LT-08663 Vilnius, Lithuania (e-mail: eugenijus.manstavicius@mif.vu.lt
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Abstract

We explore the asymptotic distributions of sequences of integer-valued additive functions defined on the symmetric group endowed with the Ewens probability measure as the order of the group increases. Applying the method of factorial moments, we establish necessary and sufficient conditions for the weak convergence of distributions to discrete laws. More attention is paid to the Poisson limit distribution. The particular case of the number-of-cycles function is analysed in more detail. The results can be applied to statistics defined on random permutation matrices.

Keywords

Primary 60C05Secondary 05A1620P05

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 23 , Issue 6: Honouring the Memory of Philippe Flajolet - Part 2 , November 2014 , pp. 889 - 913
Copyright
Copyright © Cambridge University Press 2014 

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