Geodesic
Asymptotic normality of some variables connected with the cyclic structure of random permutations
Sbornik. Mathematics, Tome 28 (1976) no. 1, pp. 107-117 
Yu. V. Bolotnikov; V. N. Sachkov; V. E. Tarakanov. Asymptotic normality of some variables connected with the cyclic structure of random permutations. Sbornik. Mathematics, Tome 28 (1976) no. 1, pp. 107-117. http://geodesic.mathdoc.fr/item/SM_1976_28_1_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Asymptotic normality as $n\to\infty$ is proved for certain random variables connected with the cyclic structure of a random permutation of degree $n$, under a nonuniform probability distribution on the set of all permutations, in particular, the asymptotic normality of the number of all cycles. Bibliography: 7 titles.

[1] V. L. Goncharov, “Iz oblasti kombinatoriki”, Izv. AN SSSR, seriya matem., 8 (1944), 3–48

[2] V. N. Sachkov, “Ob ekstremalnykh tochkakh prostranstva simmetrichnykh stokhasticheskikh matrits”, Matem. sb., 96 (138) (1975), 447–457 | Zbl

[3] V. E. Tarakanov, V. P. Chistyakov, “O tsiklovoi strukture sluchainykh podstanovok”, Matem. sb., 96 (138) (1975), 594–600 | MR | Zbl

[4] V. N. Sachkov, “Otobrazheniya konechnogo mnozhestva s ogranicheniyami na kontury i vysotu”, Teoriya veroyatnostei i ee prim., XVII:4 (1972), 679–694

[5] Dzh. Riordan, Vvedenie v kombinatornyi analiz, IL, Moskva, 1963

[6] M. A. Evgrafov, Asimptoticheskie otsenki i tselye funktsii, Fizmatgiz, Moskva, 1962 | MR

[7] J. H. Curtiss, “A note on the theory of moment generating functions”, Ann. Math. Statist., 13:3 (1942), 430–433 | DOI | MR | Zbl