Geodesic
On the cycle structure of random permutations
Sbornik. Mathematics, Tome 25 (1975) no. 4, pp. 559-565 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Suppose a probability distribution is given on the set $S_n$ of all permutations of degree $n$. The authors solve the problem of the joint distribution of the random variables $\alpha_1,\dots,\alpha_s$, where $\alpha_i$ is the number of cycles of length $i$ in a permutation from $S_n$, in a series of cases, when the initial distribution is not uniform on all of $S_n$ but on certain special subsets of it. In these cases it is shown that in the limit as $n\to\infty$ the random variables $\alpha_1,\dots,\alpha_s$ are independent and each of them has a Poisson distribution. Cases in which no joint limit distribution exists are also noted. Bibliography: 4 titles. 
@article{SM_1975_25_4_a6,
     author = {V. E. Tarakanov and V. P. Chistyakov},
     title = {On~the cycle structure of random permutations},
     journal = {Sbornik. Mathematics},
     pages = {559--565},
     year = {1975},
     volume = {25},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1975_25_4_a6/}
}
TY  - JOUR
AU  - V. E. Tarakanov
AU  - V. P. Chistyakov
TI  - On the cycle structure of random permutations
JO  - Sbornik. Mathematics
PY  - 1975
SP  - 559
EP  - 565
VL  - 25
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1975_25_4_a6/
LA  - en
ID  - SM_1975_25_4_a6
ER  - 
%0 Journal Article
%A V. E. Tarakanov
%A V. P. Chistyakov
%T On the cycle structure of random permutations
%J Sbornik. Mathematics
%D 1975
%P 559-565
%V 25
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1975_25_4_a6/
%G en
%F SM_1975_25_4_a6
V. E. Tarakanov; V. P. Chistyakov. On the cycle structure of random permutations. Sbornik. Mathematics, Tome 25 (1975) no. 4, pp. 559-565. http://geodesic.mathdoc.fr/item/SM_1975_25_4_a6/

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

[2] V. F. Kolchin, V. P. Chistyakov, “Kombinatornye zadachi teorii veroyatnostei”, Itogi nauki i tekhniki. Teoriya veroyatnostei. Matem. stat. Teor. kib., 11, VINITI, M., 1974, 5–45

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

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