Geodesic
On the rate of convergence of quasigroup convolutions of probability distributions
Diskretnaya Matematika, Tome 34 (2022) no. 3, pp. 160-171

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We consider one of the possible generalizations of sums of independent random variable to the case of operations on a finite set, namely quasigroup “sums” that use quasigroup operations on a given finite set instead of the addition operation. For quasigroup “sums” that contain $n$ independent identically distributed random variables we prove that the rate of convergence of distributions to uniform distribution is exponential in $n$.
Keywords: random variable sum, finite quasigroup, limit distribution, convergence rate 
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     author = {A. D. Yashunskii},
     title = {On the rate of convergence of quasigroup convolutions of probability distributions},
     journal = {Diskretnaya Matematika},
     pages = {160--171},
     publisher = {mathdoc},
     volume = {34},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2022_34_3_a11/}
}
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A. D. Yashunskii. On the rate of convergence of quasigroup convolutions of probability distributions. Diskretnaya Matematika, Tome 34 (2022) no. 3, pp. 160-171. http://geodesic.mathdoc.fr/item/DM_2022_34_3_a11/