We consider the Wigner minor process, i.e. the eigenvalues of an \(N\times N\) Wigner matrix \(H^{(N)}\) together with the eigenvalues of all its \(n\times n\) minors, \(H^{(n)}\) , \(n\le N\) . The top eigenvalues of \(H^{(N)}\) and those of its immediate minor \(H^{(N-1)}\) are very strongly correlated, but this correlation becomes weaker for smaller minors \(H^{(N-k)}\) as k increases. For the GUE minor process the critical transition regime around \(k\sim N^{2/3}\) was analyzed by Forrester and Nagao (Forrester and Nagao, J. Stat. Mech. (08): P08011, 2011) providing an explicit formula for the nontrivial joint correlation function. We prove that this formula is universal, i.e. it holds for the Wigner minor process. Moreover, we give a complete analysis of the sub- and supercritical regimes both for eigenvalues and for the corresponding eigenvector overlaps, thus we prove the decorrelation transition in full generality.
