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Zap. Nauchn. Sem. POMI, 2012, Volume 408, Pages 62–73 (Mi znsl5492)  

This article is cited in 8 scientific papers (total in 8 papers)

Bounds on the maximum of the density for sums of independent random variables

S. G. Bobkova, G. P. Chistyakovb

a School of Mathematics, University of Minnesota, Minneapolis, MN, USA
b Fakultät für Mathematik, Universität Bielefeld, Bielefeld, Deutschland

Abstract: Sublinear bounds on the maximum of the density for sums of independent random variables are given in terms of the maxima of the densities of the summands.

Key words and phrases: sums of independent random variables, maximum of the density.

Full text: PDF file (236 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences (New York), 2014, 199:2, 100–106

Bibliographic databases:

UDC: 519.2
Received: 15.10.2012

Citation: S. G. Bobkov, G. P. Chistyakov, “Bounds on the maximum of the density for sums of independent random variables”, Probability and statistics. Part 18, Zap. Nauchn. Sem. POMI, 408, POMI, St. Petersburg, 2012, 62–73; J. Math. Sci. (N. Y.), 199:2 (2014), 100–106

Citation in format AMSBIB
\Bibitem{BobChi12}
\by S.~G.~Bobkov, G.~P.~Chistyakov
\paper Bounds on the maximum of the density for sums of independent random variables
\inbook Probability and statistics. Part~18
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 408
\pages 62--73
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5492}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3032208}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 199
\issue 2
\pages 100--106
\crossref{https://doi.org/10.1007/s10958-014-1836-9}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902247780}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Wang L., Madiman M., “Beyond the Entropy Power Inequality, Via Rearrangements”, IEEE Trans. Inf. Theory, 60:9 (2014), 5116–5137  crossref  mathscinet  zmath  isi  scopus
    2. Bobkov S.G., Chistyakov G.P., “on Concentration Functions of Random Variables”, J. Theor. Probab., 28:3 (2015), 976–988  crossref  mathscinet  zmath  isi  elib  scopus
    3. 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
    4. P. Xu, J. Melbourne, M. Madiman, “A min-entropy power inequality for groups”, 2017 IEEE International Symposium on Information Theory (ISIT), IEEE International Symposium on Information Theory, IEEE, 2017, 674–678  isi
    5. P. Xu, J. Melbourne, M. Madiman, “Infinity-Renyi entropy power inequalities”, 2017 IEEE International Symposium on Information Theory (ISIT), IEEE International Symposium on Information Theory, IEEE, 2017  isi
    6. Marsiglietti A., Melbourne J., “A Renyi Entropy Power Inequality For Log-Concave Vectors and Parameters in [0,1]”, 2018 IEEE International Symposium on Information Theory (Isit), IEEE International Symposium on Information Theory, IEEE, 2018, 1964–1968  isi
    7. Li J., Melbourne J., “Further Investigations of the Maximum Entropy of the Sum of Two Dependent Random Variables”, 2018 IEEE International Symposium on Information Theory (Isit), IEEE International Symposium on Information Theory, IEEE, 2018, 1969–1972  isi
    8. Marsiglietti A., Melbourne J., “On the Entropy Power Inequality For the Renyi Entropy of Order [0,1]”, IEEE Trans. Inf. Theory, 65:3 (2019), 1387–1396  crossref  mathscinet  zmath  isi  scopus
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