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On the volume of the intersection of two $L^ n_ p$ balls


Authors: G. Schechtman and J. Zinn
Journal: Proc. Amer. Math. Soc. 110 (1990), 217-224
MSC: Primary 46B20
DOI: https://doi.org/10.1090/S0002-9939-1990-1015684-0
MathSciNet review: 1015684
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Abstract: In this note we prove that the proportion of the volume left in the $L_p^n$ ball after removing a $t$-multiple of the $L_q^n$ ball is of order ${e^{ - c{t^p}{n^{p/q}}}}.$


References [Enhancements On Off] (What's this?)

  • Vitali D. Milman and Gideon Schechtman, Asymptotic theory of finite-dimensional normed spaces, Lecture Notes in Mathematics, vol. 1200, Springer-Verlag, Berlin, 1986. With an appendix by M. Gromov. MR 856576

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Article copyright: © Copyright 1990 American Mathematical Society