Geodesic
On the rate of convergence of the distribution of the number of cycles of given length in a random permutation with known number of cycles to the limit distributions
Diskretnaya Matematika, Tome 18 (2006) no. 3, pp. 61-76 
E. V. Cherepanova. On the rate of convergence of the distribution of the number of cycles of given length in a random permutation with known number of cycles to the limit distributions. Diskretnaya Matematika, Tome 18 (2006) no. 3, pp. 61-76. http://geodesic.mathdoc.fr/item/DM_2006_18_3_a3/
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     title = {On the rate of convergence of the distribution of the number of cycles of given length in a~random permutation with known number of cycles to the limit distributions},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let on the set $S_{n,N}$ of all different permutations of degree $n$ with $N$ cycles the uniform distribution be given. We obtain estimates of the rate of convergence of the distribution of the number of cycles of given length in a random permutation of $S_{n,N}$ to the limit distributions as $n,N\to\infty$ in such a way that either $n/N\to 1$ or $n/N\to\infty$.

[1] Kolchin V. F., Sevastyanov B. A., Chistyakov V. P., Sluchainye razmescheniya, Nauka, Moskva, 1976

[2] Timashev A. N., “O raspredelenii chisla tsiklov zadannoi dliny v klasse podstanovok s izvestnym chislom tsiklov”, Diskretnaya matematika, 13:4 (2001), 60–72 | Zbl

[3] Cherepanova E. V., “Predelnye raspredeleniya chisla tsiklov zadannoi dliny v sluchainoi podstanovke s izvestnym chislom tsiklov”, Diskretnaya matematika, 15:3 (2003), 128–144 | Zbl

[4] Kolchin V. F., Sluchainye otobrazheniya, Nauka, Moskva, 1984

[5] Prokhorov Yu. V., “Asimptoticheskoe povedenie binomialnogo raspredeleniya”, Uspekhi matem. nauk, 8:3 (1953), 135–142 | MR | Zbl

[6] Kolchin V. F., Sluchainye grafy, Fizmatlit, Moskva, 2004

[7] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady, Nauka, Moskva, 1981