A vectorial Slepian type inequality. Applications

Khaoulani, B.

doi:10.1090/S0002-9939-1993-1159173-4

A vectorial Slepian type inequality. Applications
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Proc. Amer. Math. Soc. 118 (1993), 95-102 Request permission

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

Séries de variables aléatoires Gaussiennes à valeurs dans

Application aux produits d’espaces de Wiener

Régularité des trajectoires des fonctions aléatoires Gaussiennes

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