Random matrix with dependent entries

Question

Suppose I have a vector $v=(v_i)_{i=1,\dots,n}$ with independent entries in $[0,1]$, and let $\mathbb{E}[v]=(\mathbb{E}[v_i])_{i=1,\dots,n}$ the vector with expected values of $v$. Is it possible to obtain a bound on the spectral matrix norm $$ \lVert v v^T-\mathbb{E}[v]\mathbb{E}[v]^T\rVert? $$ I know that if the entries of the matrix $v v^T$ would be independent, we can use results from random matrix theory to show that this norm would be smaller than some bound. However, the entries are obviously not independent, so I do not know how to proceed.