Abstract
We obtain a new upper estimate on the Euclidean diameter of the intersection of the kernel of a random matrix with iid rows with a given convex body. The proof is based on a small-ball argument rather than on concentration and thus the estimate holds for relatively general matrix ensembles.
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Notes
- 1.
We will abuse notation and not distinguish between the measure μ and the random vector X that has μ as its law.
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Acknowledgements
The work was partially supported by the Mathematical Sciences Institute – The Australian National University and by the Israel Science Foundation grant 900/10.
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Mendelson, S. (2014). A Remark on the Diameter of Random Sections of Convex Bodies. In: Klartag, B., Milman, E. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2116. Springer, Cham. https://doi.org/10.1007/978-3-319-09477-9_25
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DOI: https://doi.org/10.1007/978-3-319-09477-9_25
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