I have a NxN covariance matrix with 1's in the diagonals and x's everywhere else.

I know the eigenvalue's are [(N-1)(x+1)], (1-x), (1-x),.......

I know the eigenvector for the largest eigenvalue is [1,-1,-1,.....]

Question is:

As N -> infinity, what fraction of the total variance is explained by the largest eigenvalue?