Talagrand, M. A new isoperimetric inequality for product measure and the tails of sums of independent random variables. (English) Zbl 0760.60005 Geom. Funct. Anal. 1, No. 2, 211-223 (1991). In [author, Ann. Probab. 17, No. 4, 1546-1570 (1989; Zbl 0692.60016)] a new method to study the tails of a sum of independent mean zero Banach- space valued random variables have been developed. The method was based on isoperimetric inequalities for product measure. In the paper under review a new isoperimetric inequality is proved and an improvement of the basic estimate of a tail of a sum of independent random variables from the previous paper is given. Reviewer: R.Norvaiša (Ottawa) Cited in 4 Documents MSC: 60B05 Probability measures on topological spaces 46B09 Probabilistic methods in Banach space theory Keywords:tails of a sum of independent mean zero Banach-space valued random variables; isoperimetric inequalities for product measure Citations:Zbl 0692.60016 PDFBibTeX XMLCite \textit{M. Talagrand}, Geom. Funct. Anal. 1, No. 2, 211--223 (1991; Zbl 0760.60005) Full Text: DOI EuDML References: [1] W. Johnson, G. Schechtman, Remarks on Talagrand’s deviation inequality for Rademacher functions. Longhorn notes, Lecture Notes in Math, Springer Verlag, to appear. · Zbl 0753.60024 [2] S. Kwapien and J. Szulga, Hypercontraction methods for comparison of moments of random series in normed spaces. Ann. Probab, to appear. [3] M. Ledoux, M. Talagrand, Some applications of isoperimetric methods to strong limit theorems for sums of independent random variables. Ann. Probab. 18 (1990), 754–789. · Zbl 0713.60005 · doi:10.1214/aop/1176990857 [4] M. Talagrand, An isoperimetric theorem on the cube and the Kintchine-Kahane inequalities. Proc. Amer. Mat. Soc. 104 (1988), 905–909. · Zbl 0691.60015 · doi:10.1090/S0002-9939-1988-0964871-7 [5] M. Talagrand, Isoperimetry and integrability of the sum of independent Banach-space valued random variables. Ann. Probab. 17 (1989), 1546–1570. · Zbl 0692.60016 · doi:10.1214/aop/1176991174 [6] M. Talagrand, Some isoperimetric inequalities and their applications, to appear in Proceedings of ICM, Kyoto (1990). · Zbl 0713.60005 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.