RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Diskr. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Diskr. Mat., 2016, Volume 28, Issue 3, Pages 14–25 (Mi dm1380)  

Asymptotics of conditional probabilities of succesful allocation of random number of particles into cells

A. I. Afonina, I. R. Kayumov, A. N. Chuprunov

Kazan (Volga Region) Federal University

Abstract: The article is devoted to the memory of Valentin Fedorovich Kolchin.\qquad\qquad\qquad\qquad\qquad\linebreak Let $\zeta$, $\zeta_i$ ($i\inN$) be independent identically distributed nonnegative integer-valued random variables, $(\eta_{i1},…, \eta_{iN})$ be the fillings of cells in the generalized scheme of allocation of $\zeta_i$ particles into $N$ cells, $1\le i\le n$, for fixed $Z_n=(\zeta_1,\ldots,\zeta_n)$ these allocation schemes are independent. We consider the conditional probabilities $P(A_{n, N} |Ż_n)$ of the event\linebreak $A_{n, N}=\{each cell in each of n allocation schemes contains no more than r particles\}$, where $r$ is some fixed number. The sufficient conditions for the convergence of the sequence $P(A_{n, N} |Ż_n)$ to a nonrandom limit with probability 1 are given. It is shown that the random variable $\ln P(A_{n, N} |Ż_n)$ is asymptotically normal. Applications of the obtained results to the noise-proof encoding are discussed.

Keywords: generalized allocation scheme, Cauchy integral, Hamming code.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00351
15-41-02433
This work was financially supported by the Russian Foundation for Basic Research, project No 14-01-00351, and by the RFBR and the Government of the Republic of Tatarstan, the project No 15-41-02433.


DOI: https://doi.org/10.4213/dm1380

Full text: PDF file (503 kB)
References: PDF file   HTML file

English version:
Discrete Mathematics and Applications, 2017, 27:5, 277–286

Bibliographic databases:

UDC: 519.212.2
Received: 12.01.2015
Revised: 26.07.2016

Citation: A. I. Afonina, I. R. Kayumov, A. N. Chuprunov, “Asymptotics of conditional probabilities of succesful allocation of random number of particles into cells”, Diskr. Mat., 28:3 (2016), 14–25; Discrete Math. Appl., 27:5 (2017), 277–286

Citation in format AMSBIB
\Bibitem{AfoKayChu16}
\by A.~I.~Afonina, I.~R.~Kayumov, A.~N.~Chuprunov
\paper Asymptotics of conditional probabilities of succesful allocation of random number of particles into cells
\jour Diskr. Mat.
\yr 2016
\vol 28
\issue 3
\pages 14--25
\mathnet{http://mi.mathnet.ru/dm1380}
\crossref{https://doi.org/10.4213/dm1380}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3643043}
\elib{http://elibrary.ru/item.asp?id=27349804}
\transl
\jour Discrete Math. Appl.
\yr 2017
\vol 27
\issue 5
\pages 277--286
\crossref{https://doi.org/10.1515/dma-2017-0028}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000414954500002}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85031788510}


Linking options:
  • http://mi.mathnet.ru/eng/dm1380
  • https://doi.org/10.4213/dm1380
  • http://mi.mathnet.ru/eng/dm/v28/i3/p14

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Дискретная математика
    Number of views:
    This page:450
    Full text:25
    References:30
    First page:37

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020