Geodesic
Convex polyhedra of distributions preserved by operations over a finite field
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2017), pp. 54-58 
A. D. Yashunskii. Convex polyhedra of distributions preserved by operations over a finite field. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2017), pp. 54-58. http://geodesic.mathdoc.fr/item/VMUMM_2017_4_a8/
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     title = {Convex polyhedra of distributions preserved by operations over a finite field},
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Voir la notice de l'article provenant de la source Math-Net.Ru

We construct families of polytopes in the space of probability distributions over a finite field, which are preserved, i.e. when adding or multiplying independent random variables with distributions from the constructed set, one obtains a result whose distribution belongs to the set as well.

[1] Yashunskii A.D., “O bespovtornykh preobrazovaniyakh sluchainykh velichin nad konechnymi polyami”, Diskretn. matem., 27:3 (2015), 145–157 | DOI | MR

[2] Belousov V.D., Osnovy teorii kvazigrupp i lup, Nauka, M., 1967 | MR

[3] Rado R., “An inequality”, J. London Math. Soc., 27 (1952), 1–6 | DOI | MR | Zbl

[4] Emelichev V.A., Kovalev M.M., Kravtsov M.K., Mnogogranniki, grafy, optimizatsiya (kombinatornaya teoriya mnogogrannikov), Nauka, M., 1981 | MR

[5] Hall M., “An existence theorem for latin squares”, Bull. Amer. Math. Soc., 51:6 (1945), 387–388 | DOI | MR | Zbl

[6] Kaluzhnin L.A., Suschanskii V.I., Preobrazovaniya i perestanovki, Nauka, M., 1979 | MR