Given a $n\times n$ symmetric random matrix such that
- all diagonal elements are all fixed as $0$.
- all other elements in the upper triangle are uniform random variables over $[0,1]$. all values in the lower triangle are set accordingly to ensure symmetry.
The question is,
Is there known exact/or asymptotic ($n \to \infty$) formula for distribution of the largest eigenvalue of such matrix?
*Now as suggested by the comment, the exact formula seems not exist, but still hope someone could help with the asymptotic case.
I am not familiar with random matrix theory, but I think this kind of matrix is not uncommon, and there hopefully should have been some result. Thanks!