On Statistics of Permutations Chosen From the Ewens Distribution. (November 2014)

• Record Type: Journal Article
• Authors: BAKSHAJEVA, TATJANA; MANSTAVIČIUS, EUGENIJUS; Broutin, Nicolas; Fill, James Allen; Nebel, Markus; Ward, Mark Daniel
• Is Part Of: Combinatorics, probability and computing. Volume 23:Number 6(2014:Nov.)
• Page Start: 889
• Page End: 913
• Publication Date: 2014-11
• Subjects: Combinatorial analysis -- Periodicals; Probabilities -- Periodicals; Computer science -- Mathematics -- Periodicals; 511.6
• DOI: 10.1017/S0963548314000376
• Languages: English
• ISSNs: 0963-5483

Abstract

<abstract abstract-type="normal"> <title> <x content-type="archive" xml:space="preserve">Abstract</x> </title> <p>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.</p> </abstract>