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In the current paper we consider a Wigner matrix and consider an analyticfunction of polynomial growth on a set containing the support of thesemicircular law in its interior. We prove that the linear spectral statisticscorresponding to the function and the point process at the edge of the Wignermatrix are asymptotically independent when the entries of the Wigner matrix aresub-Gaussian. The main ingredient of the proof is based on a recent paper byBanerjee [6]. The result of this paper can be viewed as a first step to findthe joint distribution of eigenvalues in the bulk and the edge.

Independence of linear spectral statistics and the point process at the edge of Wigner matrices