Spectrum of Wigner matrices with dependent entries

We study the limiting spectral distribution (LSD) of Wigner matrices whose entries come from a stationary process. We provide an explicit description of the moments of the limiting measure. The description of the LSD can also be made via its Cauchy transform which is characterized as the solution of a functional equation. In two special cases, we get a neat description of the LSD - one as a free product convolution of two distributions, and the other one as a dilation of the Wigner semicircular law.

This is a joint work with Arijit Chakrabarty and Deepayan Sarkar.