The Circular Law for Random Matrices with Intra-row Dependence

Chris Connell, Pawan Patel

Published 2018-01-15Version 1

We consider the problem of determining the limiting spectral distribution for random matrices whose row distributions are permitted to have limited dependence. We assume mild moment conditions and give an extension of the Mar\v{c}enko-Pastur theorem for this context. The main new feature here are geometric conditions on the distributions which allow us to extend the circular law to this setting.