This is an announcement for the paper "Poincar'{e} type inequalities on the discrete cube and in the CAR algebra" by Limor Ben-Efraim and Francoise Lust-Piquard.

Abstract: We prove Lp Poincare inequalities for functions on the discrete cube and their discrete gradient. We thus recover an exponential inequality and the concentration phenomenon for the uniform probability on the cube first obtained by Bobkov and Gotze. Inequalities involving the discrete gradient and powers of the discrete Laplacian are also considered, for the Lp norm or more general ones. Similar results hold true, replacing functions on the cube by elements of the CAR algebra and considering the annihilation operators and the number operator.

Archive classification: Functional Analysis

Mathematics Subject Classification: 46E39, 46L57, 46L51

The source file(s), poincare-cube-final.tex: 85518 bytes, is(are) stored in gzipped form as 0702233.gz with size 21kb. The corresponding postcript file has gzipped size 182kb.

Submitted from: limor_be@cs.huji.ac.il

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http://front.math.ucdavis.edu/math.FA/0702233

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http://arXiv.org/abs/math.FA/0702233

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