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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 441, Pages 204–209 (Mi znsl6234)  

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

Bound for the maximal probability in the Littlewood–Offord problem

A. Yu. Zaitsevab

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b St. Petersburg State University, St. Petersburg, Russia
Full-text PDF (161 kB) Citations (5)
References:
Abstract: The paper deals with studying a connection of the Littlewood–Offord problem with estimating the concentration functions of some symmetric infinitely divisible distributions. It is shown that the values at zero of the concentration functions of weighted sums of i.i.d. random variables may be estimated by the values at zero of the concentration functions of symmetric infinitely divisible distributions with the Lévy spectral measures which are multiples of the sum of delta-measures at $\pm$weights involved in constructing the weighted sums.
Key words and phrases: concentration functions, inequalities, the Littlewood–Offord problem, sums of independent random variables.
Received: 18.11.2015
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 219, Issue 5, Pages 743–746
DOI: https://doi.org/10.1007/s10958-016-3143-0
Bibliographic databases:
Document Type: Article
UDC: 519.2
Language: Russian
Citation: A. Yu. Zaitsev, “Bound for the maximal probability in the Littlewood–Offord problem”, Probability and statistics. Part 22, Zap. Nauchn. Sem. POMI, 441, POMI, St. Petersburg, 2015, 204–209; J. Math. Sci. (N. Y.), 219:5 (2016), 743–746
Citation in format AMSBIB
\Bibitem{Zai15}
\by A.~Yu.~Zaitsev
\paper Bound for the maximal probability in the Littlewood--Offord problem
\inbook Probability and statistics. Part~22
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 441
\pages 204--209
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6234}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3504506}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 219
\issue 5
\pages 743--746
\crossref{https://doi.org/10.1007/s10958-016-3143-0}
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  • https://www.mathnet.ru/eng/znsl/v441/p204
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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