B0505
Title: Random matrices with independent entries: Beyond non-crossing partitions
Authors: Priyanka Sen - Indian Statistical Institute, Kolkata (India) [presenting]
Abstract: The scaled standard Wigner matrix is known to have the semi-circular distribution as its LSD. The moments of the LSD are described with the help of non-crossing pair partitions. There have been several extensions of this result. We shall discuss the LSD of symmetric matrices with independent entries under certain moment assumptions and find a suitable set of partitions that help describe the moments of the LSD. The set of partitions found is in general larger than the class of non-crossing partitions and pose some interesting combinatorial questions. The LSD result will also help us bring several existing LSD results under one umbrella. For example, results on the standard Wigner matrix, the adjacency matrix of a sparse homogeneous Erdos-Renyi graph, heavy-tailed Wigner matrix, some banded Wigner matrices, Wigner matrices with variance profile follow from our result.
