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A B
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  • Member for 3 years, 7 months
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Is $\mathbb E\left[\frac{d}{||x||_1^2}\right]=O(1)$ for all $d\in\mathbb R^+$, where $x\in S^{d-1}$ is a random $d$-dimensional unit vector?
Apr 26, 2021
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Let $a\in S^d$, $b\in S^{d-1}$ be uniform on the spheres. How to show $\mathbb E[\frac{||a||_1}{\sqrt {d+1}}] \le\mathbb E[\frac{||b||_1}{\sqrt d}]$?
Apr 28, 2021
question
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Let $G_{(n)}=(G_1,\ldots,G_n)$ be a vector of $n$ i.i.d. normal vars. How to show $(d+1)(d-1)E[1/||G_{(d+1)}||_1^2]\ge d(d-2)E[1/||G_{(d)}||_1^2]?$
Apr 29, 2021