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Modified Paouris Inequality

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Book cover Geometric Aspects of Functional Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2116))

Abstract

The Paouris inequality gives the large deviation estimate for Euclidean norms of log-concave vectors. We present a modified version of it and show how the new inequality may be applied to derive tail estimates of l r -norms and suprema of norms of coordinate projections of isotropic log-concave vectors.

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References

  1. R. Adamczak, R. Latała, A.E. Litvak, K. Oleszkiewicz, A. Pajor N. Tomczak-Jaegermann, A short proof of Paouris’ inequality. Can. Math. Bull. 57, 3–8 (2014)

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  2. R. Adamczak, R. Latała, A.E. Litvak, A. Pajor, N. Tomczak-Jaegermann, Tail estimates for norms of sums of log-concave random vectors. Proc. Lond. Math. Soc. 108, 600–637 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  3. R.E. Barlow, A.W. Marshall, F. Proschan, Properties of probability distributions with monotone hazard rate. Ann. Math. Stat. 34, 375–389 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  4. C. Borell, Convex measures on locally convex spaces. Ark. Math. 12, 239–252 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  5. S. Brazitikos, A. Giannopoulos, P. Valettas, B.H. Vritsiou, Geometry of Isotropic Convex Bodies. Mathematical Surveys and Monographs vol. 196 (American Mathematical Society, Providence, 2014)

    Google Scholar 

  6. R. Latała, Order statistics and concentration of l r norms for log-concave vectors. J. Funct. Anal. 261, 681–696 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. R. Latała, Weak and strong moments of random vectors, in: Marcinkiewicz Centenary Volume, Banach Center Publications vol. 95 (Polish Academy of Sciences, Warsaw, 2011), pp. 115–121

    Google Scholar 

  8. G. Paouris, Concentration of mass on convex bodies. Geom. Funct. Anal. 16, 1021–1049 (2006)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

Research supported by NCN grant 2012/05/B/ST1/00412.

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Authors and Affiliations

  1. Institute of Mathematics, University of Warsaw, Banacha 2, 02-097, Warszawa, Poland

    Rafał Latała

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  1. Rafał Latała
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Correspondence to Rafał Latała .

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Editors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel

    Bo'az Klartag

  2. Technion - Israel Institute of Technology, Haifa, Israel

    Emanuel Milman

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Latała, R. (2014). Modified Paouris Inequality. In: Klartag, B., Milman, E. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2116. Springer, Cham. https://doi.org/10.1007/978-3-319-09477-9_19

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