Geodesic
On~the cycle structure of random permutations
Sbornik. Mathematics, Tome 25 (1975) no. 4, pp. 559-565

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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. 
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     author = {V. E. Tarakanov and V. P. Chistyakov},
     title = {On~the cycle structure of random permutations},
     journal = {Sbornik. Mathematics},
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     volume = {25},
     number = {4},
     year = {1975},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1975_25_4_a6/}
}
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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/