Abstract

It is well known that the limit eigenvalue distribution of the scaled standard Wigner matrix is the semi-circular distribution whose 2k-th moment equals the number of non-crossing pair-partitions of {1,2, ..., 2k}. There are several specific extensions of this result in the literature, including the sparse case. We discuss a broad extension by relaxing significantly the i.i.d. assumption. The limiting spectral distribution then involve a larger class of partitions. In the process we show how some new sets of partitions gain importance. Several existing and new results for their band and sparse versions, as well as for matrices with continuous and discrete variance profile follow as special cases.