L.I.F.E.: and Halloween Law

Abstract

After obtaining the results for normalized spectral functions (n.s.f.) of a single symmetric, non-symmetric and unitary random matrix, we now move in this paper toward the main goal, namely to the most general solution of the problem of limit theorems in the theory of random matrices: to find limit distributions of n.s.f. of random matrices , , j, k, p = 1, 2, . . .] where ƒ(x1, x2, . . .) is an analytical function and , j = 1, 2, . . . , are independent ACE (Asymptotically Constant Entries)-random matrices (in particular, unitary random matrices). Using the canonical equation K91, we derive the so-called L.I.F.E.-Law.