PUBLISHED PAPERS #04.18
| Ibrokhimali Normatov, Ruzmat Dadazhanov. Classification of a Quadratic Stochastic Operator Built on a Disconnected Graph by Binomial Distributions |
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| Abstract. The article is devoted to the construction of quadratic stochastic binomial distribution operators on nonlinear finite graphs in an (n-1)-dimensional simplex and is studied by dividing the constructed operators into classes. The construction of quadratic stochastic operators is given, quadratic stochastic operators constructed by binomial distributions are described. The main classes of quadratic stochastic operators are determined: non-degenerate, completely positive, irreducible. A theorem is proved, where necessary and sufficient conditions are established, under which quadratic stochastic operators are completely positive. |
| Keywords: graph, probability measure, quadratic operator, non-degenerate, completely positive, irreducible |
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| DOI: https://doi.org/10.30546/MaCoSEP2025.1484 |