Geodesic
Limit Poisson law for the distribution of the number of components in generalized allocation scheme
Diskretnaya Matematika, Tome 29 (2017) no. 4, pp. 143-157

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We consider problems on the convergence of distributions of the total number of components and numbers of components with given volume to the Poisson law. Sufficient conditions of such convergence are given. Our results generalize known statemets on the limit Poisson laws of the number of components (cycles, unrooted and rooted trees, blocks and other structures) in the corresponding generalized allocation schemes.
Keywords: generalized allocation scheme, Poisson distribution, components, cycles, blocks, trees, saddle-point method. 
@article{DM_2017_29_4_a9,
     author = {A. N. Timashev},
     title = {Limit {Poisson} law for the distribution of the number of components in generalized allocation scheme},
     journal = {Diskretnaya Matematika},
     pages = {143--157},
     publisher = {mathdoc},
     volume = {29},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2017_29_4_a9/}
}
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A. N. Timashev. Limit Poisson law for the distribution of the number of components in generalized allocation scheme. Diskretnaya Matematika, Tome 29 (2017) no. 4, pp. 143-157. http://geodesic.mathdoc.fr/item/DM_2017_29_4_a9/