Chapter 3 Random Vectors in High Dimensions
3.1 Concentration of the norm
Theorem. 3.1.1. Concentration of the norm
$X=(X_1,…,X_n)\in\mathbb{R}^n$ s.t. $X_i$ are independent, subgaussian, with $E[X_i^2]=1$ then $\Vert\Vert X\Vert^2-\sqrt(n)\Vert_{\phi_2}\le CK^2$, where $K=\max_i\Vert X_i\Vert_{\psi_2}$ and $C$ is an absolute constrant.
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