Let $A$ be a random $m$-by-$n$ matrix with iid $N(0,1)$ entries, $m$ and $n$ large with $n/m \longrightarrow \alpha \in (0, 1)$ . Let $\|A\|_2$ be the largest singular value of $A$  (i.e the spectral norm of $A$) and let $t \ge 0$.

>**Question.** What is a good upper bound for $\mathbb E_A[e^{-t\|A\|_2}]$ ?