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Zap. Nauchn. Sem. POMI, 2013, Volume 412, Pages 121–137 (Mi znsl5644)  

This article is cited in 5 scientific papers (total in 5 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

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.

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English version:
Journal of Mathematical Sciences (New York), 2015, 204:1, 78–89

Bibliographic databases:

UDC: 519.2
Received: 18.11.2012

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://www.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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. S. Eliseeva, F. Götze, A. Yu. Zaitsev, “Estimates for the concentration functions in the Littlewood–Offord problem”, J. Math. Sci. (N. Y.), 206:2 (2015), 146–158  mathnet  crossref
    2. Yu. S. Eliseeva, A. Yu. Zaitsev, “On the Littlewood–Offord problem”, J. Math. Sci. (N. Y.), 214:4 (2016), 467–473  mathnet  crossref  mathscinet
    3. A. Yu. Zaitsev, “Bound for the maximal probability in the Littlewood–Offord problem”, J. Math. Sci. (N. Y.), 219:5 (2016), 743–746  mathnet  crossref  mathscinet
    4. F. Götze, Yu. S. Eliseeva, A. Yu. Zaitsev, “Arak inequalities for concentration functions and the Littlewood–Offord problem”, Theory Probab. Appl., 62:2 (2018), 196–215  mathnet  crossref  crossref  mathscinet  isi  elib
    5. M. A. Lifshits, Ya. Yu. Nikitin, V. V. Petrov, A. Yu. Zaitsev, A. A. Zinger, “Toward the history of the Saint Petersburg school of probability and statistics. I. Limit theorems for sums of independent random variables”, Vestn. St Petersb. Univ. Math., 51:2 (2018), 144–163  crossref  crossref  mathscinet  zmath  isi  elib  scopus
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