# PrincipAl Eigenvector of a Random Matrix

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:

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

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Principal ! Don't confuse principal bundle and maximum principle. – Denis Serre Apr 21 '12 at 11:26
This is one of the most annoying misspellings, I am tempted to vote to close just for that. – Igor Rivin Apr 25 '12 at 16:56