Geodesic
$p$-adic behavior of Bernoulli probabilities
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 4, pp. 839-845

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We study the standard Bernoulli probabilistic scheme for independent random variables (the symmetric case). As usual, we are interested in limits of probabilities when the number of trails approaches infinity. However, these limits are considered with respect to the $p$-adic metric. This is a sufficiently exotic metric and it is surprising that ordinary (classical) probabilities have limits with respect to this metric. Thus we found a new asymptotic of the classical Bernoulli probabilities which was not visible before.
Keywords: Bernoulli probability, $p$-adic numbers, metric
Mots-clés : Bernoulli scheme, binomial coefficients. 
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     author = {A. Yu. Khrennikov},
     title = {$p$-adic behavior of {Bernoulli} probabilities},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {839--845},
     publisher = {mathdoc},
     volume = {42},
     number = {4},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_4_a15/}
}
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A. Yu. Khrennikov. $p$-adic behavior of Bernoulli probabilities. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 4, pp. 839-845. http://geodesic.mathdoc.fr/item/TVP_1997_42_4_a15/