Gaussian operator norm conjecture for arbitrary matrices

Let $p$ and $q$ satisfy $p\le 2\le q$, and let $A=(a_{ij})_{i\le m,j\le n}$ be a deterministic $m\times n$ matrix. Write $p^*$ for the Hölder conjugate of $p$, and let $G_A=(a_{ij}g_{ij})_{i,j}$, where the $g_{ij}$ are independent standard Gaussian random variables. The notation $u\sim_{p,q}v$ means that $u$ and $v$ are comparable up to positive constants depending only on $p$ and $q$. Gaussian operator norm conjecture. For every such $p,q$ and $A$, \

\mathbb E\\|G_A\\|_{p\to q}\sim_{p,q} \max_i \\|(a_{ij})_j\\|_{p^*}+\max_j \\|(a_{ij})_i\\|_q+\mathbb E\max_{i,j}|a_{ij}g_{ij}|. \

This conjecture seeks sharp two-sided estimates for expected Gaussian operator norms beyond the spectral and extremal $ll_p$ cases; before this work, comparable bounds for arbitrary matrices in the remaining ranges were open up to logarithmic factors or known only in special tensor-product cases.