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Poincaré type inequalities on the discrete cube and in the CAR algebra
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  • Published: 18 August 2007

Poincaré type inequalities on the discrete cube and in the CAR algebra

  • L. Ben Efraim1,2 &
  • F. Lust-Piquard3 

Probability Theory and Related Fields volume 141, pages 569–602 (2008)Cite this article

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  • 13 Citations

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Abstract

We prove L p Poincaré inequalities with suitable dimension free constants for functions on the discrete cube {−1, 1}n. As well known, such inequalities for p an even integer allow to recover an exponential inequality hence the concentration phenomenon first obtained by Bobkov and Götze. We also get inequalities between the L p norms of \( \left\vert \nabla f\right\vert \) and \(\Delta ^{\alpha }f,\alpha > 0;\) moreover L p spaces may be replaced by more general ones. Similar results hold true, replacing functions on the cube by matrices in the *-algebra spanned by n fermions and the L p norm by the Schatten norm C p .

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Authors and Affiliations

  1. The Hebrew University, Jerusalem, Israel

    L. Ben Efraim

  2. Weizmann Institute of Science, Rehovot, Israel

    L. Ben Efraim

  3. Université de Cergy, Cergy, France

    F. Lust-Piquard

Authors
  1. L. Ben Efraim
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  2. F. Lust-Piquard
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Correspondence to L. Ben Efraim.

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Ben Efraim, L., Lust-Piquard, F. Poincaré type inequalities on the discrete cube and in the CAR algebra. Probab. Theory Relat. Fields 141, 569–602 (2008). https://doi.org/10.1007/s00440-007-0094-x

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  • Received: 07 February 2007

  • Revised: 08 June 2007

  • Published: 18 August 2007

  • Issue Date: July 2008

  • DOI: https://doi.org/10.1007/s00440-007-0094-x

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Keywords

  • Primary: 60E15
  • Secondary: 43A70
  • 47A20
  • 46E39
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