Geodesic
Random mappings of sets with restrictions on parameters. II
Matematičeskie voprosy kriptografii, Tome 3 (2012) no. 2, pp. 97-116 
V. N. Sachkov. Random mappings of sets with restrictions on parameters. II. Matematičeskie voprosy kriptografii, Tome 3 (2012) no. 2, pp. 97-116. http://geodesic.mathdoc.fr/item/MVK_2012_3_2_a4/
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     author = {V. N. Sachkov},
     title = {Random mappings of sets with restrictions on {parameters.~II}},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2012_3_2_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Graphs corresponding to the binary shift registers of length $l$ with a random Boolean feedback function of given weight are considered. Formulas for the conditional distribution, mean, variance and binomial moments of the number of initial vertices are obtained. Conditions ensuring the convergence of distributions of the number cycle vertices to the Rayleigh distribution are given. For random mapping with fixed points the limiting bivariate distribution of the number of successors and of the length of corresponding cycle for a given vertex is found.

[1] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, Mir, M., 1967 | MR | Zbl

[2] Sachkov V. N., “Sluchainye preobrazovaniya mnozhestv s ogranicheniyami na parametry. I”, Matematicheskie voprosy kriptografii, 3:1 (2012), 125–144

[3] Harris B., “Probability distributions related to random mappings”, Ann. Math. Stat., 31:4 (1960), 1045–1062 | DOI | MR | Zbl