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Sudakov-type minoration for gaussian chaos processes

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Abstract

Consider a setA of symmetricn×n matricesa=(a i,j) i,j≤n . Consider an independent sequence (g i) i≤n of standard normal random variables, and letM=Esupa∈A|Σi,j⪯nai,jgigj|. Denote byN 2(A, α) (resp.N t(A, α)) the smallest number of balls of radiusα for thel 2 norm ofR n 2 (resp. the operator norm) needed to coverA. Then for a universal constantK we haveα(logN 2(A, α))1/4≤KM. This inequality is best possible. We also show that forδ≥0, there exists a constantK(δ) such thatα(logN t≤K(δ)M.

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References

  1. C. Borell,On polynomial chaos and integrability, Prop. Math. Statist.3 (1984), 191–203.

    MathSciNet  Google Scholar 

  2. M. Marcus and G. Pisier,Characterizations of almost surely continuous p-stable random Fourier series and strongly stationary processes, Acta Math.152 (1984), 245–301.

    Article  MATH  MathSciNet  Google Scholar 

  3. M. Ledoux and M. Talagrand,Probability in Banach Spaces, Springer-Verlag, Berlin, 1991.

    MATH  Google Scholar 

  4. G. Pisier,Volume Inequalities in the Geometry of Banach Spaces, Cambridge University Press, 1989.

  5. A. Pajor and N. Tomczak-Jaegermann,Subspaces of small codimension of finite dimensional Banach Spaces, Proc. Am. Math. Soc.97 (1986), 637–642.

    Article  MATH  MathSciNet  Google Scholar 

  6. M. Talagrand,Regularity of Gaussian Processes, Acta Math.155 (1987), 99–149.

    Article  MathSciNet  Google Scholar 

  7. M. Talagrand,Necessary conditions for sample boundedness of p-stable processes, Annals Probab.16 (1988), 1584–1595.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. University of Paris VI, 75230, Paris Cedex 05, France

    Michel Talagrand

  2. The Ohio State University, 43210, Columbus, OH, USA

    Michel Talagrand

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  1. Michel Talagrand
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Work partially supported by an N.S.F. grant.

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Talagrand, M. Sudakov-type minoration for gaussian chaos processes. Israel J. Math. 79, 207–224 (1992). https://doi.org/10.1007/BF02808216

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  • DOI: https://doi.org/10.1007/BF02808216

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