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Majorization of Gaussian processes and geometric applications
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  • Published: June 1992

Majorization of Gaussian processes and geometric applications

  • Yehoram Gordon1 

Probability Theory and Related Fields volume 91, pages 251–267 (1992)Cite this article

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Summary

Let (x *i ) ni=1 denote the decreasing rearrangement of a sequence of real numbers (x i ) ni=1 . Then for everyi≠j, and every 1≦k≦n, the 2-nd order partial distributional derivatives satisfy the inequality,\(\frac{{\partial ^2 }}{{\partial x_i \partial x_j }}\left( {\sum\limits_{l = 1}^k {x_l^* } } \right) \leqq 0\). As a consequence we generalize the theorem due to Fernique and Sudakov. A generalization of Slepian's lemma is also a consequence of another differential inequality. We also derive a new proof and generalizations to volume estimates of intersecting spheres and balls in ℝn proved by Gromov.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Technion-Israel Institute of Technology, 32000, Haifa, Israel

    Yehoram Gordon

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  1. Yehoram Gordon
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Additional information

Supported by NSF grant # DMS 8909745, and the USA-Israel Binational Science Foundation grant # 86-00074, and grant for the Promotion of Research at the Technion

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Cite this article

Gordon, Y. Majorization of Gaussian processes and geometric applications. Probab. Th. Rel. Fields 91, 251–267 (1992). https://doi.org/10.1007/BF01291425

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  • Received: 21 April 1991

  • Revised: 04 September 1991

  • Issue Date: June 1992

  • DOI: https://doi.org/10.1007/BF01291425

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Keywords

  • Real Number
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Gaussian Process
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