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What condition on random matrix can preserve sub-Gaussian property?

If you only have the hypothesis of sub-Gaussianity, this is the best you can do. Work in dimension $n=1$ for simplicity, let $X\sim N(0,1)$, and let $A$ be independent of $X$. If $AX$ is to be sub-...
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Induced distribution from random unitary

Assuming real matrix elements, the distribution of the $N=d_1d_2$ elements $v_1,v_2,\ldots v_N$ of the $d_1\times d_2$ matrix $V$ is a delta function, $$P(v_1,v_2,\ldots v_N)\propto\delta\left(1-\sum_{...

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