Abstract
We present a simple proof to a fact recently established in Guédon et al. (Commun Contemp Math (to appear, 2018). arXiv:1811.12007): let ξ be a symmetric random variable that has variance 1, let Γ = (ξ ij) be an N × n random matrix whose entries are independent copies of ξ, and set X 1, …, X N to be the rows of Γ. Then under minimal assumptions on ξ and as long as N ≥ c 1n, with high probability
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Notes
- 1.
A centred random variable is L-sub-Gaussian if for every p ≥ 2, \(\|\xi \|{ }_{L_p} \leq L \sqrt {p}\|\xi \|{ }_{L_2}\).
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Mendelson, S. (2020). On the Geometry of Random Polytopes. In: Klartag, B., Milman, E. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2266. Springer, Cham. https://doi.org/10.1007/978-3-030-46762-3_8
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DOI: https://doi.org/10.1007/978-3-030-46762-3_8
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