Let $A$ be a random matrix, let $\mathbf{x}$ be the singular vector associated with $\|A\|$. Let $\bar A$ be the entry wise expectation of $A$, and let  $\mathbf{\bar x}$ be the singular vector associated with $\|\bar A\|$.

Given $\epsilon > 0$, what conditions are necessary to have:

$$P [ \|\mathbf{x} - \mathbf{\bar x}\| < \epsilon] < \epsilon ?$$