Non-Hermitean Wishart random matrices (I)
Abstract
A non-Hermitean extension of paradigmatic Wishart random matrices is introduced to set up a theoretical framework for statistical analysis of (real, complex and real quaternion) stochastic time series representing two "remote" complex systems. The first paper in a series provides a detailed spectral theory of non-Hermitean Wishart random matrices composed of complex valued entries. The great emphasis is placed on an asymptotic analysis of the mean eigenvalue density for which we derive, among other results, a complex-plane analogue of the Marchenko-Pastur law. A surprising connection with a class of matrix models previously invented in the context of quantum chromodynamics is pointed out.
Cite
@article{arxiv.1006.3096,
title = {Non-Hermitean Wishart random matrices (I)},
author = {Eugene Kanzieper and Navinder Singh},
journal= {arXiv preprint arXiv:1006.3096},
year = {2011}
}
Comments
published version: 29 pages, 4 figures; references added