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 Teor. Veroyatnost. i Primenen., 1997, Volume 42, Issue 4, Pages 839–845 (Mi tvp2620)

Short Communications

$p$-adic behavior of Bernoulli probabilities

A. Yu. Khrennikovab

a Mathematical Institute, Bochum University, Germany
b Moscow State Institute of Electronic Technology (Technical University)

Abstract: 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, Bernoulli scheme, $p$-adic numbers, metric, binomial coefficients.

DOI: https://doi.org/10.4213/tvp2620

Full text: PDF file (374 kB)

English version:
Theory of Probability and its Applications, 1998, 42:4, 689–694

Bibliographic databases:

Citation: A. Yu. Khrennikov, “$p$-adic behavior of Bernoulli probabilities”, Teor. Veroyatnost. i Primenen., 42:4 (1997), 839–845; Theory Probab. Appl., 42:4 (1998), 689–694

Citation in format AMSBIB
\Bibitem{Khr97} \by A.~Yu.~Khrennikov \paper $p$-adic behavior of Bernoulli probabilities \jour Teor. Veroyatnost. i Primenen. \yr 1997 \vol 42 \issue 4 \pages 839--845 \mathnet{http://mi.mathnet.ru/tvp2620} \crossref{https://doi.org/10.4213/tvp2620} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1618782} \zmath{https://zbmath.org/?q=an:0917.60037} \transl \jour Theory Probab. Appl. \yr 1998 \vol 42 \issue 4 \pages 689--694 \crossref{https://doi.org/10.1137/S0040585X97976581} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000079809500012} 

• http://mi.mathnet.ru/eng/tvp2620
• https://doi.org/10.4213/tvp2620
• http://mi.mathnet.ru/eng/tvp/v42/i4/p839

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. A. Yu. Khrennikov, Sh. Yamada, “On the concept of random sequence with respect to $p$-adic valued probabilities”, Theory Probab. Appl., 49:1 (2005), 65–76
2. Khrennikov A.Yu., Mukhamedov F.M., Mendes J.F.F., “On p–adic Gibbs measures of the countable state Potts model on the Cayley tree”, Nonlinearity, 20:12 (2007), 2923–2937
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