Geodesic
The occurrence of a gigantic component in a random permutation with a known number of cycles
Diskretnaya Matematika, Tome 15 (2003) no. 3, pp. 145-159.

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We give conditions for emergence of a giant cycle in a random permutation with a given number of cycles and obtain limit distributions of the maximum cycle lengths in all domains of variation of the parameters. 
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N. I. Kazimirov. The occurrence of a gigantic component in a random permutation with a known number of cycles. Diskretnaya Matematika, Tome 15 (2003) no. 3, pp. 145-159. http://geodesic.mathdoc.fr/item/DM_2003_15_3_a9/

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