Noncommutative Burkholder/Rosenthal inequalities II: Applications
By Marius Junge, Quanhua Xu. 2007
97 citations recorded by the source corpus.
We show norm estimates for the sum of independent random variables in noncommutative Lp-spaces for 1 < p < ∞, following our previous work. These estimates generalize the classical Rosenthal inequality in the commutative case. As applications, we derive an equivalence for the p-norm of the singular values of a random matrix with independent entries, and characterize those symmetric subspaces and unitary ideals which can be realized as subspaces of a noncommutative Lp for 2 < p < ∞.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b210e752b90ada47d4f0aa0f813a85b78b137dbd
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In Applied Mathematics
- Javier Parcet
- Marius Junge
- Quanhua Xu
- Narcisse Randrianantoanina
- Tao Mei
- Uffe Haagerup
- Joel A. Tropp
- Richard Y. Chen
In Mathematical Physics
- Javier Parcet
- Marius Junge
- Quanhua Xu
- Tao Mei
- Narcisse Randrianantoanina
- Uffe Haagerup
- Joel A. Tropp
- Richard Y. Chen
Citations in the corpus
- Noncommutative Riesz transforms -- a probabilistic approach (2008, background): “Let us recall some definitions from [JX08].”
- Matrix concentration inequalities via the method of exchangeable pairs (2012, methodology): “Other matrix extensions of the BDG inequality appear in the work of Pisier–Xu [40] and the work of Junge–Xu [21, 22].”
- Conditioned square functions for noncommutative martingales (2005, background): “lassical case, for 1 < p < ∞, M ⊂ BMO(M) ⊂ Lp(M,τ). For more information on martingale BMO-spaces, we refer to [16, 17, 23, 27]. In this section, we consider the case of independence studied in [18, 35]. Definition5.1. (i) Let N be a von Neumann subalgebra of M and let EN be the associated tra”
- Rosenthal Type inequalities for free chaos. (2005, background): “analogue of Rosenthal’s inequality [17, 18].”
- User-Friendly Tail Bounds for Sums of Random Matrices (2010, background): “Some of these results have been applied to the study of random matrices; see [27] for an example.”
- A reduction method for noncommutative L_p-spaces and applications (2008, methodology): “These include the Doob inequality in [Ju1], the Burkholder/Rosenthal inequalities in [JX1, JX2 ], the weak type (1,1) inequality for martingale transforms in [R1] and the Gundy decomposition in [PaR].”