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How much are increasing sets positively correlated?

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Abstract

Two upward directed sets of sequences of zeroes and ones are positively correlated. We provide a lower bound on the correlation, in function of how much the two sets simultaneously depend on the same coordinates.

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References

  1. J. Kahn, G. Kalai, andN. Linial:The influence of variables on Boolean functions, Proc. 29th IEEE FOCS, 1988, 58–80.

  2. M. Ledoux andM. Talagrand:Probability in Banach space, Springer Verlag, 1991.

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Author information

Authors and Affiliations

  1. Equipe d'Analyse-Tour 46 U.A. au C.N.R.S. no 754, Université Paris VI, 4 Pl Jussieu, 75230, Paris, Cedex 05, France

    Michel Talagrand

  2. Department of Mathematics, 231 West 18th Avenue, 43210, Columbus, Ohio, USA

    Michel Talagrand

Authors
  1. Michel Talagrand
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Work partially supported by an NSF grant.

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Talagrand, M. How much are increasing sets positively correlated?. Combinatorica 16, 243–258 (1996). https://doi.org/10.1007/BF01844850

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  • DOI: https://doi.org/10.1007/BF01844850

Mathematics Subject Classification (1991)