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. 
@article{MVK_2020_11_a4,
     author = {V. A. Kopytcev},
     title = {Limit theorems on the normal distribution for the number of solutions of nonlinear inclusions},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {77--96},
     publisher = {mathdoc},
     volume = {11},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2020_11_a4/}
}
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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/