rademacher_sampled_matrix_noncommutative_khintchine_diagonal_gram_bound_q2

Corrected (q≥2) noncommutative Khintchine / Lust-Picquard–Pisier–Buchholz bound for the Rademacher coordinate sum $S_\varepsilon=p^{-1}\sum_{(i,j)\in\Omega}\varepsilon_{ij}X_{ij}e_ie_j^\top$. There is an absolute constant $C>0$ such that for every $\beta>2$ and every $q$ with $q\ge 2$ and $q\ge\beta\log(\max(n_1,n_2))$, the $q$-th Schatten moment satisfies $\mathbb{E}_\varepsilon\,\|S_\varepsilon\|_{S_q}^q \le (C\sqrt q\,\max(G_{\mathrm{row}},G_{\mathrm{col}}))^q$, where $G_{\mathrm{row}},G_{\mathrm{col}}$ are the diagonal Gram Schatten-$q$ norms $\|(\sum_{ij}A_{ij}A_{ij}^\top)^{1/2}\|_{S_q}$ and $\|(\sum_{ij}A_{ij}^\top A_{ij})^{1/2}\|_{S_q}$ of the coordinate matrices $A_{ij}=p^{-1}[(i,j)\in\Omega]X_{ij}e_ie_j^\top$. This is the corrected form of the $q\ge 1$ node: the noncommutative Khintchine inequality (Lust-Picquard–Pisier; Buchholz, constant $2^{-1/4}\sqrt{\pi/e}$) is valid for Schatten exponents $2\le q<\infty$, so the genuine hypothesis is $q\ge 2$ (Candès–Recht 2009, arXiv:0805.4471, Lemma 6.1, §6.1, p.24).