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 $\mathbb E_A[e^{-t\sigma_1(A)}]$ ?
Estimate $\mathbb E_A[e^{-t\|A\|_2}]$, for $t\ge0$ and random m by n matrix with iid entries with law $N(0,1)$
dohmatob
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