High-dimensional $p$-norms

Gérard Biau, David D. M. Mason

Let $\bX=(X_1, \hdots, X_d)$ be a ${\mathbb{R}}^d$-valued random vector with i.i.d. components, and let $\Vert\bX\Vert_p= (\sum_{j=1}^d|X_j|^p)^{1/p}$ be its $p$-norm, for $p>0$. The…