Abstract
We construct families of polyhedra in the space of probability distributions over a finite field, which are preserved, i.e., adding or multiplying independent random variables with distributions from the constructed set, the resulting distribution belongs to the same set.
References
A. D. Yashunskii “On Read-Once Transformations of Random Variables over Finite Fields,” Diskr. Matem. 27 (3), 145 (2015) [Discrete Math. and Appl. 25 (5), 311 (2015)].
V. D. Belousov, Fundamentals of the Theory of Quasigroups and Loops (Nauka, Moscow, 1967) [in Russian].
R. Rado, “An Inequality,” J. London Math. Soc. 27, 1 (1952).
V. A. Emelichev, M. M. Kovalev, and M. K. Kravtsov, Polyhedra, Graphs, and Optimization (Combinatorial Theory of Polyhedra) (Nauka, Moscow, 1981) [in Russian].
M. Hall, “An Existence Theorem for Latin Squares,” Bull. Amer. Math. Soc. 51 (6), 387 (1945).
L. A. Kaluzhnin and V. I. Sushchanskii, Transformations and Permutations (Nauka, Moscow, 1979; [in Russian]).
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Original Russian Text © A.D. Yashunskii, 2017, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2017, Vol. 72, No. 4, pp. 54–58.
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Yashunskii, A.D. Convex polyhedra of distributions preserved by operations over a finite field. Moscow Univ. Math. Bull. 72, 165–168 (2017). https://doi.org/10.3103/S0027132217040052
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DOI: https://doi.org/10.3103/S0027132217040052