Entrywise concentration of a Gaussian Gram matrix
= Entrywise concentration of a Gaussian Gram matrix
For a $d\times p$ matrix of independent standard normal entries and $0<t<1$, diagonal entries of $A^TA/d-I$ have two-sided tails bounded by $2e^{-dt^2/8}$, while off-diagonal entries have tails bounded by $2e^{-dt^2/4}$. A <union bound> over $p$ diagonal entries and $p(p-1)/2$ distinct off-diagonal entries controls their common <entrywise maximum norm>.