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

DOI10.1007/s00440-007-0094-xzbMath1141.60005arXivmath/0702233OpenAlexW4300900786MaRDI QIDQ929378

L. Ben Efraim, Françoise Lust-Piquard

Publication date: 17 June 2008

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702233

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Dilations, extensions, compressions of linear operators (47A20) Analysis on specific locally compact and other abelian groups (43A70) Sobolev (and similar kinds of) spaces of functions of discrete variables (46E39)

Related Items (14)

Discrete Riesz transforms and sharp metric \(X_p\) inequalities ⋮ Subgaussian 1-cocycles on discrete groups ⋮ Hamming cube and martingales ⋮ Interpolation between modified logarithmic Sobolev and Poincaré inequalities for quantum Markovian dynamics ⋮ Tail spaces estimates on Hamming cube and Bernstein-Markov inequality ⋮ Heat-smoothing for holomorphic subalgebras of free group von Neumann algebras ⋮ Talagrand's influence inequality revisited ⋮ Exponential integrability in Gauss space ⋮ Polynomial inequalities on the Hamming cube ⋮ Discrete logarithmic Sobolev inequalities in Banach spaces ⋮ Square functions and the Hamming cube: duality ⋮ Poincaré type inequalities for group measure spaces and related transportation cost inequalities ⋮ Dimension independent Bernstein-Markov inequalities in Gauss space ⋮ Noncommutative martingale deviation and Poincaré type inequalities with applications

Cites Work

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• The little Grothendieck theorem and Khintchine inequalities for symmetric spaces of measurable operators
• Generalized analyticity in UMD spaces
• Non commutative Khintchine and Paley inequalities
• Some remarks on interpolation theorems and the boundness or the triangular projection in unitary matrix spaces
• Riesz transforms associated with the number operator on the Walsh system and the fermions
• Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
• Optimal hypercontractivity for Fermi fields and related non-commutative integration inequalities
• Quantum probability for probabilists.
• Optimal Constants in Khintchine Type Inequalities for Fermions, Rademachers and q-Gaussian Operators

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