Operator Khintchine inequality in non-commutative probability

By A. Buchholz. 2001

83 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2bed9adadb0077113a716dfffdaa36a3b6262756

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Joel A. Tropp
2. Marius Junge
3. Quanhua Xu
4. Per-Gunnar Martinsson
5. Javier Parcet
6. E.J. Candes
7. B. Recht
8. Roman Vershynin

In Mathematical Physics

1. Joel A. Tropp
2. Marius Junge
3. Javier Parcet
4. Quanhua Xu
5. E.J. Candes
6. Narcisse Randrianantoanina
7. Per-Gunnar Martinsson
8. B. Recht

In Statistics and Probability

1. Joel A. Tropp
2. Per-Gunnar Martinsson
3. Marius Junge
4. E.J. Candes
5. Martin J. Wainwright
6. Javier Parcet
7. Arkadi Nemirovski
8. Aharon Ben-Tal

Citations in the corpus

• Norms of Random Submatrices and Sparse Approximation (2008, unknown): “2 but relies on a sharp noncommutative Khintchine inequality [2].”
• Compressive Sensing with structured random matrices (2012, background): “The proof follows the ideas of Buchholz [16].”
• Rosenthal Type inequalities for free chaos. (2005, background): “A. Buchholz, Norm of convolution by operator-valued functions on free groups.”
• Sums of random Hermitian matrices and an inequality by Rudelson (2010, background): “Better estimates for c, and thus for the constant in Rudelson’s bound, can be obtained from the work of Buchholz [3].”
• An Introduction to Matrix Concentration Inequalities (2015, unknown): “See the papers [116, 29, 30] or [118, Cor.”
• Introduction to the non-asymptotic analysis of random matrices (2010, methodology): “The optimal value of Bp was computed by Buchholz [13, 14]; see [62, Section 6.5] for an thorough introduction to Buchholz’s argument.”
• Self-regularity - a new paradigm for primal-dual interior-point algorithms (2002, background): “Man-Cho So who brought to our attention the results of [78, 93, 35], which allow to justify easily the validity of Conjecture 10.”
• Robust Optimization (2021, background): “Proof is readily given by the following deep result from Functional Analysis due to Lust-Piquard [55], Pisier [69] and Buchholz [29], see [83, Proposition 10]: Let !!, $ = 1, .”
• Approximation properties and absence of Cartan subalgebra for free Araki-Woods factors (2010, unknown): “This formula expresses W ( e 1 ⊗ · · · ⊗ e n ) as an element of T ( H ) and has many consequences such as Khintchine type inequalities in [5, 25, 4] for instance.”
• Exact Matrix Completion via Convex Optimization (2008, methodology): “The following theorem was originally proven by Lust-Picquard [25], and was later sharpened by Buchholz [9].”
• Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions (2009, background): “ RANDOMIZED ALGORITHMS FOR MATRIX APPROXIMATION 71 The heavy lifting is accomplished by means of the following result, due to Rudelson [114], which depends on the noncommutative Khintchine inequality [19,91]. Proposition B.3 (Rudelson’s Lemma). Let {aj} ⊂ Ck be a sequence of vectors, and let {cj} be”