In the current paper we consider a Wigner matrix and consider an analytic
function of polynomial growth on a set containing the support of the
semicircular law in its interior. We prove that the linear spectral statistics
corresponding to the function and the point process at the edge of the Wigner
matrix are asymptotically independent when the entries of the Wigner matrix are
sub-Gaussian. The main ingredient of the proof is based on a recent paper by
Banerjee . The result of this paper can be viewed as a first step to find
the joint distribution of eigenvalues in the bulk and the edge.