The DOI matches its Crossref record; 27 of the 27 references it cites were found in a registry or an index.
User-Friendly Tail Bounds for Sums of Random Matrices
Open accessAbstract
This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the large-deviation behavior of the maximum eigenvalue of the sum. Tail bounds for the norm of a sum of random rectangular matrices follow as an immediate corollary. The proof techniques also yield some information about matrix-valued martingales.In other words, this paper provides noncommutative generalizations of the classical bounds associated with the names Azuma, Bennett, Bernstein, Chernoff, Hoeffding, and McDiarmid. The matrix inequalities promise the same diversity of application, ease of use, and strength of conclusion that have made the scalar inequalities so valuable.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Horn, R. A., & Johnson, C. R. (1985) · Cambridge University Press eBooks · doi:10.1017/cbo9780511810817 · Cited by 10,280
Motwani, R., & Raghavan, P. (1995) · Cambridge University Press eBooks · doi:10.1017/cbo9780511814075 · Cited by 5,123
Halko, N., Martinsson, P. G., & Tropp, J. A. (2011) · SIAM Review · doi:10.1137/090771806 · Cited by 4,002
Self-citationA Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
Chernoff, H. (1952) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729330 · Cited by 3,550
Large Deviations Techniques and Applications
Dembo, A., & Zeitouni, O. (1998) · Springer eBooks · doi:10.1007/978-1-4612-5320-4 · Cited by 3,019
Bhatia, R. (1997) · Graduate Texts in Mathematics · doi:10.1007/978-1-4612-0653-8 · Cited by 2,336
Functions of Matrices: Theory and Computation
Higham, N. J. (2008) · doi:10.1137/1.9780898717778 · Cited by 2,113
Sparsity and incoherence in compressive sampling
Candès, E., & Romberg, J. (2007) · Inverse Problems · doi:10.1088/0266-5611/23/3/008 · Cited by 2,075
Ledoux, M., & Talagrand, M. (1991) · doi:10.1007/978-3-642-20212-4 · Cited by 1,160
Introduction to Operator Space Theory
Pisier, G. (2003) · Cambridge University Press eBooks · doi:10.1017/cbo9781107360235 · Cited by 742
Cited by
Compressed Sensing Off the Grid
Tang, G., Bhaskar, B. N., Shah, P., & Recht, B. (2013) · IEEE Transactions on Information Theory · doi:10.1109/tit.2013.2277451 · Cited by 1,163
Matrix Completion Methods for Causal Panel Data Models
Athey, S., Bayati, M., Doudchenko, N., Imbens, G., & Khosravi, K. (2018) · doi:10.3386/w25132 · Cited by 497
Communication-Efficient Distributed Optimization using an Approximate Newton-type Method
Shamir, O., Srebro, N., & Zhang, T. (2013) · arXiv · doi:10.48550/arxiv.1312.7853 · Cited by 424
Fast community detection by SCORE
Jin, J. (2015) · The Annals of Statistics · doi:10.1214/14-aos1265 · Cited by 302
Complete Dictionary Recovery Over the Sphere I: Overview and the Geometric Picture
Sun, J., Qu, Q., & Wright, J. (2017) · IEEE Transactions on Information Theory · doi:10.1109/tit.2016.2632162 · Cited by 213
Metadata
- Authors
- Tropp, J. A.
- Venue
- Foundations of Computational Mathematics
- Published
- 2011-08-02
- Volume
- 12
- Issue
- 4
- Pages
- 389-434
- ISSN
- 1615-3375 (ISSN-L)
- 1615-3383
- OpenAlex
- W2107411554
- Cited by
- 718
- References
- 27
- FWCI
- 61.23
- Type
- book chapter
- Language
- en
- Open access
- hybrid
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: User-Friendly Tail Bounds for Sums of Random Matrices. https://app.cochat.ai/papers/10.1007/s10208-011-9099-z
- The paper
- Tropp, J. A. (2012). User-Friendly Tail Bounds for Sums of Random Matrices. Foundations of Computational Mathematics. https://doi.org/10.1007/s10208-011-9099-z
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
