Geodesic
Limit theorems for~a~random covering of~a~finite setand for~the~number of~solutions of~a~system of~random equations
Teoriâ veroâtnostej i ee primeneniâ, Tome 41 (1996) no. 2, pp. 272-283

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The paper deals with the problem of covering a finite set by its random subsets selected at random and independently. The probability laws of the selection of the random sets are allowed to vary from trial to trial which is essentially new for the problem under consideration. The principal result is a Poisson limit theorem for the number of uncovered points. This theorem is illustrated by two schemes of group allocation of particles and is used to show that the number of solutions of a consistent random equation system with respect to the binary vector of unknowns has asymptotically logarithmic Poisson distribution.
Mots-clés : group allocation of particles, Poisson limit theorem
Keywords: the number of empty cells, random equation systems. 
@article{TVP_1996_41_2_a2,
     author = {V. G. Mikhailov},
     title = {Limit theorems for~a~random covering of~a~finite setand for~the~number of~solutions of~a~system of~random equations},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {272--283},
     publisher = {mathdoc},
     volume = {41},
     number = {2},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1996_41_2_a2/}
}
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V. G. Mikhailov. Limit theorems for~a~random covering of~a~finite setand for~the~number of~solutions of~a~system of~random equations. Teoriâ veroâtnostej i ee primeneniâ, Tome 41 (1996) no. 2, pp. 272-283. http://geodesic.mathdoc.fr/item/TVP_1996_41_2_a2/