The question: Let $A$ be the matrix whose each element is an independently generated random variable which is uniform on $[0,1]$. One can see that the eigenvalues of $A$ will be distinct almost surely. Let $\delta = \min_{i,j} |\lambda_i(A) - \lambda_j(A)|$ be the smallest distance between any two eigenvalues of $A$ in the complex plane. What sort of lower bounds does $\delta$ satisfy with high probability?

Background: looking at the literature, it seems that for some symmetric random matrices $A$ the question has been settled, in the sense that the exact distribution of $\delta$ is known. This does not, however, seem to apply to the non-symmetric case above, and it seems reasonable to guess that the exact distribution of $\delta$ for the random matrix I am asking about is an open question.

However, here I am asking for something much less than an exact distribution of $\delta$ -- for example, can one make a statement along the lines of $P(\delta \geq 1/n^{10}) \geq 1-1/n^{0.1}$, or something like that?