Let $A$ be a random $m$-by-$n$ matrix with iid $N(0,1)$ entries. Let $\sigma_1(A)$ be the largest singular value of $A$ and let $t \ge 0$. >**Question.** What is the the value (of good upper bound) of $\mathbb E_A[e^{-t\sigma_1(A)}]$ ?