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Zapiski Nauchnykh Seminarov POMI, 2013, Volume 420, Pages 50–69 (Mi znsl5726)  
This article is cited in 13 scientific papers (total in 13 papers)

Estimates for the concentration functions in the Littlewood–Offord problem

Yu. S. Eliseevaa, F. Götzeb, A. Yu. Zaitsevac

a St. Petersburg State University, St. Petersburg, Russia
b Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
c St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (292 kB) Citations (13)
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Abstract: Let $X,X_1,\ldots,X_n$ be independent identically distributed random variables. In this paper we study the behavior of the concentration functions of the weighted sums $\sum_{k=1}^na_kX_k$ with respect to the arithmetic structure of coefficients $a_k$. Such concentration results recently became important in connection with investigations about singular values of random matrices. In this paper we formulate and prove some refinements of a result of Vershynin (2011).
Key words and phrases: concentration functions, inequalities, the Littlewood–Offord problem, sums of independent random variables.
Received: 29.10.2013
English version:
Journal of Mathematical Sciences (New York), 2015, Volume 206, Issue 2, Pages 146–158
DOI: https://doi.org/10.1007/s10958-015-2299-3
Bibliographic databases:
Document Type: Article
UDC: 519
Language: Russian
Citation: Yu. S. Eliseeva, F. Götze, A. Yu. Zaitsev, “Estimates for the concentration functions in the Littlewood–Offord problem”, Probability and statistics. Part 20, Zap. Nauchn. Sem. POMI, 420, POMI, St. Petersburg, 2013, 50–69; J. Math. Sci. (N. Y.), 206:2 (2015), 146–158
Citation in format AMSBIB
\Bibitem{EliGotZai13}
\by Yu.~S.~Eliseeva, F.~G\"otze, A.~Yu.~Zaitsev
\paper Estimates for the concentration functions in the Littlewood--Offord problem
\inbook Probability and statistics. Part~20
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 420
\pages 50--69
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5726}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 206
\issue 2
\pages 146--158
\crossref{https://doi.org/10.1007/s10958-015-2299-3}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84953351752}
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    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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