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

2007/02/08 by L. Ben Efraim, Ben-Efraim, Limor, Lust-Piquard, Francoise
Mathematics · #46E39 #46L51 #46L57 #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Random Matrices and Applications #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.math/0702233

openalex publication_date 2007/02/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• Quantum Probability for Probabilists

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