Geodesic
Limit theorems on the normal distribution for the number of solutions of nonlinear inclusions
Matematičeskie voprosy kriptografii, Tome 11 (2020), pp. 77-96.

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For a given subset $B$ of linear space $K^T$ over the field $K=GF(2)$ we study the distribution of the number $\xi$ of solutions of the system formed by inclusions $A_1x+A_2f(x)\in B$, $ x\in K^n\backslash \{0^n\}$, where $A_1$ and $A_2$ are random $T\times n$ and $T\times m$ matrices over $K$ with independend elements and $f(x)=$ $(f_1 (x),\ldots,f_m (x))\colon K^{n}\longrightarrow K^{m}$ is a given nonlinear mapping. Sufficient conditions for the convergence of distribution of $\xi$ to the standard normal distribution are obtained. 
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     title = {Limit theorems on the normal distribution for the number of solutions of nonlinear inclusions},
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V. A. Kopytcev. Limit theorems on the normal distribution for the number of solutions of nonlinear inclusions. Matematičeskie voprosy kriptografii, Tome 11 (2020), pp. 77-96. http://geodesic.mathdoc.fr/item/MVK_2020_11_a4/

[1] Kopyttsev V. A., Mikhailov V. G., “O raspredelenii chisel reshenii sluchainykh vklyuchenii”, Matematicheskie voprosy kriptografii, 2:2 (2011), 81–107

[2] Kopyttsev V. A., Mikhailov V. G., “Otsenki dlya minimalnogo rasstoyaniya sluchainogo lineinogo koda”, Diskretnaya matematika, 27:2 (2015), 45–55

[3] Kopyttsev V. A., Mikhailov V. G., “Yavnye otsenki tochnosti puassonovskoi approksimatsii dlya raspredeleniya chisla reshenii sluchainykh vklyuchenii”, Matematicheskie voprosy kriptografii, 6:1 (2015), 34–57 | MR

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

[5] Sachkov V. N., Veroyatnostnye metody v kombinatornom analize, Nauka, M., 1978, 288 pp.

[6] Janson S., “Normal convergence by higher semiinvariants with applications to sums of dependent random variables and random graphs”, Ann. Probab., 16:1 (1988), 305–312 | DOI | MR | Zbl

[7] Shiryaev A. N., Veroyatnost–1, MTsNMO, M., 2007