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Teoriya Veroyatnostei i ee Primeneniya, 2012, Volume 57, Issue 4, Pages 768–777
DOI: https://doi.org/10.4213/tvp4479 (Mi tvp4479) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Short Communications

Estimates of the concentration functions of weighted sums of independent random variables

Yu. S. Eliseevaa, A. Yu. Zaitsevb

a Saint-Petersburg State University
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (180 kB) Citations (10)
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DOI: https://doi.org/10.4213/tvp4479
Abstract: Let $X_1,\dots,X_n$ be independent and identially distributed random variables. The paper deals with obtaining upper bounds on the concentration function of the weighted sums $\sum_{k=1}^na_kX_k$ based on the coefficients $a_k$, $1\leqslant k\leqslant n$. Results obtained in this paper improve over the recent works in [O. Friedland and S. Sodin, C. R., Math., Acad. Sci. Paris 345, No. 9, 513–518 (2007; Zbl 1138.60023)] and [M. Rudelson and R. Vershynin, Adv. Math. 218, No. 2, 600–633 (2008; Zbl 1139.15015), Commun. Pure Appl. Math. 62, No. 12, 1707–1739 (2009; Zbl 1183.15031)].
Keywords: concentration functions; inequalities; sums of independent random variables; Littlewood–Offord problem.
Received: 26.02.2012
English version:
Theory of Probability and its Applications, 2013, Volume 57, Issue 4, Pages 670–678
DOI: https://doi.org/10.1137/S0040585X97986254
Bibliographic databases:
Document Type: Article
MSC: 60E15
Language: Russian
Citation: Yu. S. Eliseeva, A. Yu. Zaitsev, “Estimates of the concentration functions of weighted sums of independent random variables”, Teor. Veroyatnost. i Primenen., 57:4 (2012), 768–777; Theory Probab. Appl., 57:4 (2013), 670–678
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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