Geodesic
Discrete limit laws for additive functions on the symmetric group
Communications in Mathematics, Tome 13 (2005) no. 1, pp. 47-55.

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Inspired by probabilistic number theory, we establish necessary and sufficient conditions under which the numbers of cycles with lengths in arbitrary sets posses an asymptotic limit law. The approach can be extended to deal with the counts of components with the size constraints for other random combinatorial structures.
Classification : 05A16, 05D40, 60C05
Keywords: random permutation; cycle structure; Poisson distribution; factorial moment 
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Manstavičius, Eugenijus. Discrete limit laws for additive functions on the symmetric group. Communications in Mathematics, Tome 13 (2005) no. 1, pp. 47-55. http://geodesic.mathdoc.fr/item/COMIM_2005__13_1_a5/