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The distribution of Rademacher sums

Author: S. J. Montgomery-Smith
Journal: Proc. Amer. Math. Soc. 109 (1990), 517-522
MSC: Primary 60C05; Secondary 46M35, 60E15, 60G50
MathSciNet review: 1013975
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Abstract: We find upper and lower bounds for $ {\Pr(}\Sigma \pm {x_n} \geq t)$, where $ {x_1},{x_2}, \ldots $ are real numbers. We express the answer in terms of the $ K$-interpolation norm from the theory of interpolation of Banach spaces.

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  • [1] C. Bennett and R. Sharpley, Interpolation of operators, Academic Press, New York, 1988. MR 928802 (89e:46001)
  • [2] K. L. Chung, A course in probability theory, 2nd. ed., Academic Press, New York, 1974. MR 0346858 (49:11579)
  • [3] T. Holmstedt, Interpolation of quasi-normed spaces, Math. Scand. 26 (1970), 177-199. MR 0415352 (54:3440)
  • [4] J.-P. Kahane, Some random series of functions, Cambridge Stud. Adv. Math. 5, 1985. MR 833073 (87m:60119)
  • [5] P.-A. Meyer, Martingales and stochastic integrals I. Springer-Verlag, Berlin. 284, 1972. MR 0426145 (54:14091)
  • [6] S. J. Montgomery-Smith, The cotype of operators from $ C(K)$, Ph.D. thesis, Cambridge, August 1988.
  • [7] G. Pisier, De nouvelles caractérisations des ensembles de Sidon, Mathematical analysis and applications, Adv. Math. Suppl. Stud. 7B (1981), 686-725. MR 634264 (82m:43011)
  • [8] V. A. Rodin and E. M. Semyonov, Rademacher series in symmetric spaces, Analyse Math. 1 (1975), 207-222. MR 0388068 (52:8905)

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Keywords: Rademacher sum, Holmstedt's formula
Article copyright: © Copyright 1990 American Mathematical Society

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