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Zapiski Nauchnykh Seminarov POMI, 2013, Volume 412, Pages 121–137 (Mi znsl5644)  

This article is cited in 6 scientific papers (total in 6 papers)

Multivariate estimates for the concentration functions of weighted sums of independent identically distributed random variables

Yu. S. Eliseeva

St. Petersburg State University, St. Petersburg, Russia
Full-text PDF (269 kB) Citations (6)
References:
Abstract: This article is a multidimensional generalization of the results Eliseeva and Zaitsev (2012). Let $X,X_1,\ldots,X_n$ be independent identically distributed random variables. The paper deals with the question about the behavior of the concentration function of the random variable $\sum_{k=1}^na_kX_k$ according to the arithmetic structure of vectors $a_k$. Recently the interest to this question has increased significantly due to the study of distributions of eigenvalues of random matrices. In this paper we formulate and prove some refinements of the results Friedland and Sodin (2007) and Rudelson and Vershynin (2009).
Key words and phrases: multivarite concentration functions, sums of independent random variables, the Littlewood–Offord problem.
Received: 18.11.2012
English version:
Journal of Mathematical Sciences (New York), 2015, Volume 204, Issue 1, Pages 78–89
DOI: https://doi.org/10.1007/s10958-014-2188-1
Bibliographic databases:
Document Type: Article
UDC: 519.2
Language: Russian
Citation: Yu. S. Eliseeva, “Multivariate estimates for the concentration functions of weighted sums of independent identically distributed random variables”, Probability and statistics. Part 19, Zap. Nauchn. Sem. POMI, 412, POMI, St. Petersburg, 2013, 121–137; J. Math. Sci. (N. Y.), 204:1 (2015), 78–89
Citation in format AMSBIB
\Bibitem{Eli13}
\by Yu.~S.~Eliseeva
\paper Multivariate estimates for the concentration functions of weighted sums of independent identically distributed random variables
\inbook Probability and statistics. Part~19
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 412
\pages 121--137
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5644}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3073541}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 204
\issue 1
\pages 78--89
\crossref{https://doi.org/10.1007/s10958-014-2188-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84925489945}
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  • https://www.mathnet.ru/eng/znsl/v412/p121
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:234
    Full-text PDF :55
    References:48
     
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