Geodesic
On one characteristic of a random mapping with given number of cycles
Diskretnaya Matematika, Tome 18 (2006) no. 3, pp. 43-60 
I. A. Cheplyukova. On one characteristic of a random mapping with given number of cycles. Diskretnaya Matematika, Tome 18 (2006) no. 3, pp. 43-60. http://geodesic.mathdoc.fr/item/DM_2006_18_3_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the random variable equal to the number of trees of given size in the graph of a random one-to-one mapping of an $n$-element set into itself with $m$ connected components. We obtain limit theorems which describe the distribution of this characteristic in the case where $n\to\infty$, $m/\ln n\to\infty$, $m/\ln n=O(\ln n)$.

[1] Pavlov Yu. L., “Predelnye teoremy dlya chisla derevev zadannogo ob'ema v sluchainom lese”, Matem. sb., 103:3 (1977), 392–403 | MR | Zbl

[2] Pavlov Yu. L., “Asimptoticheskie raspredeleniya maksimalnogo ob'ema dereva v sluchainom lese”, Teoriya veroyatnostei i ee primeneniya, 22:3 (1977), 523–533 | MR | Zbl

[3] Pavlov Yu. L., Sluchainye lesa, Petrozavodsk, 1996

[4] Grekhem R., Knut D., Patashnik O., Konkretnaya matematika, Mir, Moskva, 1998 | MR

[5] Cheplyukova I. A., “Odin sluchai predelnogo raspredeleniya chisla tsiklicheskikh vershin v sluchainom otobrazhenii”, Diskretnaya matematika, 16:3 (2004), 76–84 | Zbl

[6] Kolchin V. F., Sluchainye grafy, Fizmatlit, Moskva, 2000

[7] Sachkov V. I., Veroyatnostnye metody v kombinatornom analize, Nauka, Moskva, 1978