Given a $n\times n$ **symmetric** random matrix such that

- all
diagonalelements are allfixedas $0$.- all other elements in the upper triangle are
uniform random variablesover $[0,1]$. 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!