Noncommutative Bennett and Rosenthal inequalities
By Marius Junge, Qiang Zeng. 2011
55 citations recorded by the source corpus.
In this paper we extend the Bernstein, Prohorov and Bennett inequalities to the noncommutative setting. In addition we provide an improved version of the noncommutative Rosenthal inequality, essentially due to Nagaev, Pinelis and Pinelis, Utev for commutative random variables. We also present new best constants in Rosenthal’s inequality. Applying these results to random Fourier projections, we recover and elaborate on fundamental results from compressed sensing, due to Candes, Romberg and Tao.
Subfields: Applied Mathematics, Computational Mechanics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/77c9b80d044b218dd3e6d4c193d4829d912c4097
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In Applied Mathematics
- Javier Parcet
- Tao Mei
- Marius Junge
- Qiang Zeng
- Quanhua Xu
- Narcisse Randrianantoanina
- A. Gonz'alez-P'erez
- Sjoerd Dirksen
In Computational Mechanics
In Statistics and Probability
- Javier Parcet
- Tao Mei
- Qiang Zeng
- Marius Junge
- Narcisse Randrianantoanina
- Quanhua Xu
- Joel A. Tropp
- Sjoerd Dirksen
Citations in the corpus
- Noncommutative martingale deviation and Poincaré type inequalities with applications (2012, background): “For independent increments this has recently been proved in [36].”
- Noncommutative Riesz transforms -- Dimension free bounds and Fourier multipliers (2014, background): “Note that EM⋊G(fjfj∗) = EM⋊G(ff∗) and EM⋊G(fj∗fj) = EM⋊G(f∗f) for all j. Moreover, we also have kfjkp = kfkp. Therefore, the second inequality follows sending m→ ∞. An improved Rosenthal’s inequality [38] actually yields kfkG p(M)⋊G ≤ C √ pkfkRC p(M)⋊G, which provides the correct order of the consta”