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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A vectorial Slepian type inequality. Applications
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by B. Khaoulani
Proc. Amer. Math. Soc. 118 (1993), 95-102
DOI: https://doi.org/10.1090/S0002-9939-1993-1159173-4

Abstract:

We prove a new inequality for Gaussian processes; this inequality implies the Chevet’s inequality and Gordon’s inequalities. Some remarks on Gaussian proofs of Dvoretzky’s theorem are given.
References
  • Louis H. Y. Chen, An inequality for the multivariate normal distribution, J. Multivariate Anal. 12 (1982), no. 2, 306–315. MR 661566, DOI 10.1016/0047-259X(82)90022-7
  • S. Chevet, Séries de variables aléatoires Gaussiennes à valeurs dans $E{\widehat \otimes _\varepsilon }F$. Application aux produits d’espaces de Wiener, Séminaire Maurey-Schwartz, exposé XiX 77/78. X. M. Fernique, Régularité des trajectoires des fonctions aléatoires Gaussiennes, Lecture Notes in Math., vol. 480, Springer-Verlag, New York, 1974.
  • Yehoram Gordon, Some inequalities for Gaussian processes and applications, Israel J. Math. 50 (1985), no. 4, 265–289. MR 800188, DOI 10.1007/BF02759761
  • Yehoram Gordon, Elliptically contoured distributions, Probab. Theory Related Fields 76 (1987), no. 4, 429–438. MR 917672, DOI 10.1007/BF00960067
  • Jean-Pierre Kahane, Une inégalité du type de Slepian et Gordon sur les processus gaussiens, Israel J. Math. 55 (1986), no. 1, 109–110 (French, with English summary). MR 858463, DOI 10.1007/BF02772698
  • V. D. Milman, A new proof of A. Dvoretzky’s theorem on cross-sections of convex bodies, Funkcional. Anal. i Priložen. 5 (1971), no. 4, 28–37 (Russian). MR 0293374
  • Gilles Pisier, Probabilistic methods in the geometry of Banach spaces, Probability and analysis (Varenna, 1985) Lecture Notes in Math., vol. 1206, Springer, Berlin, 1986, pp. 167–241. MR 864714, DOI 10.1007/BFb0076302
  • Gideon Schechtman, A remark concerning the dependence on $\epsilon$ in Dvoretzky’s theorem, Geometric aspects of functional analysis (1987–88), Lecture Notes in Math., vol. 1376, Springer, Berlin, 1989, pp. 274–277. MR 1008729, DOI 10.1007/BFb0090061
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Bibliographic Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 118 (1993), 95-102
  • MSC: Primary 60G15; Secondary 46B07, 47N30
  • DOI: https://doi.org/10.1090/S0002-9939-1993-1159173-4
  • MathSciNet review: 1159173