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On Some Extension of Feige’s Inequality

  • Krzysztof OleszkiewiczEmail author
Chapter
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Part of the Lecture Notes in Mathematics book series (LNM, volume 2050)

Abstract

An extension of the Feige inequality [Feige, SIAM J. Comput. 35,964–984 (2006)] is formulated and proved in a relatively simple way.

Keywords

Fourth Moment Method Independent Zero-mean Random Variables Extreme Point Theory Uriel Feige Berry-Esseen Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

I would like to thank Franck Barthe for a fruitful discussion which inspired my work on Feige’s inequality during my visit to Institut de Mathématiques at Université Paul Sabatier in Toulouse in May 2010. It is a pleasure to acknowledge their kind hospitality. Research partially supported by Polish MNiSzW Grant N N201 397437.

References

  1. 1.
    U. Feige, On sums of independent random variables with unbounded variance and estimating the average degree in a graph. SIAM J. Comput. 35, 964–984 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    M.G. Hahn, M.J. Klass, Uniform local probability approximations: Improvements on Berry-Esseen. Ann. Probab. 23, 446–463 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    S. He, J. Zhang, S. Zhang, Bounding probability of small deviation: A fourth moment approach. Math. Oper. Res. 35, 208–232 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    K. Oleszkiewicz, Concentration of capital – the product form of the law of large numbers in L 1. Statist. Probab. Lett. 55, 159–162 (2001)Google Scholar
  5. 5.
    V.V. Petrov, in Sums of Independent Random Variables. Ergeb. Math. Grenzgeb., vol. 82 (Springer, Berlin, 1975)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of WarsawWarsawPoland
  2. 2.Institute of MathematicsPolish Academy of SciencesWarsawPoland

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