Geodesic
On the distribution of the numbers of solutions of random inclusions
Matematičeskie voprosy kriptografii, Tome 2 (2011) no. 2, pp. 55-80 Cet article a éte moissonné depuis la source Math-Net.Ru

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For given sets $D$ and $B$ of vectors in linear spaces $V^n$ and $V^T$ over the field $K=GF(q)$ we consider the number of solutions $\xi(D,F,B)$ of the system of inclusions $x\in D$, $A_1x+A_2 f(x)\in B$, where $A_1$ and $A_2$ are random $T\times n$ and $T\times m$ matrices over $K$ with independent elements and $f\colon V^n\to V^m$ is a given mapping. Sufficient conditions for the convergence of distributions of $\xi(D,F,B)$ to the Poisson or compound Poisson distributions are found. Results are applied to the number of solutions of a system of random polynomial equations. 
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V. A. Kopytcev; V. G. Mikhailov. On the distribution of the numbers of solutions of random inclusions. Matematičeskie voprosy kriptografii, Tome 2 (2011) no. 2, pp. 55-80. http://geodesic.mathdoc.fr/item/MVK_2011_2_2_a2/

[1] Kopyttsev V. A., Mikhailov V. G., “Teoremy puassonovskogo tipa dlya chisla spetsialnykh reshenii sluchainogo lineinogo vklyucheniya”, Diskretnaya matematika, 22:2 (2010), 3–21 | MR

[2] Kopyttsev V. A., Mikhailov V. G., “Teoremy puassonovskogo tipa dlya chisla reshenii sluchainykh vklyuchenii”, Matematicheskie voprosy kriptografii, 1:4 (2010), 63–84

[3] Kopyttsev V. A., “O chisle reshenii sistem lineinykh bulevykh uravnenii v mnozhestve vektorov, obladayuschikh zadannym chislom edinits”, Diskretnaya matematika, 14:4 (2002), 87–109 | MR | Zbl

[4] Kopyttsev V. A., “O chisle reshenii sistemy sluchainykh lineinykh uravnenii”, Diskretnaya matematika, 18:1 (2006), 40–62 | Zbl

[5] Kolchin V. F., Sevastyanov B. A., Chistyakov V. P., Sluchainye razmescheniya, Nauka, M., 1976 | Zbl

[6] Sevastyanov B. A., “Predelnyi zakon Puassona v skheme summ zavisimykh sluchainykh velichin”, Teoriya veroyatn. i ee primenen., 17:4 (1972), 733–738 | MR | Zbl

[7] Mikhailov V. G., “Predelnye teoremy dlya chisla reshenii sistemy sluchainykh lineinykh uravnenii, popavshikh v zadannoe mnozhestvo”, Diskretnaya matematika, 19:1 (2007), 17–26 | MR | Zbl

[8] Masol V. I., “Teorema o predelnom raspredelenii chisla lozhnykh reshenii sistemy nelineinykh sluchainykh uravnenii”, Teoriya veroyatn. i ee primen., 43:1 (1998), 41–56 | MR | Zbl