Random ε nets and embeddings in ` N ∞ ∗
نویسندگان
چکیده
We show that, given an n-dimensional normed space X a sequence of N = (8/ε)2n independent random vectors (Xi)i=1, uniformly distributed in the unit ball of X∗, with high probability forms an ε net for this unit ball. Thus the random linear map Γ : Rn → RN defined by Γx = (〈x,Xi〉)i=1 embeds X in `∞ with at most 1+ ε norm distortion. In the case X = `2 we obtain a random 1 + ε embedding into `∞ with asymptotically best possible relation between N , n, and ε.
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تاریخ انتشار 2006