Distribution of the Smallest Eigenvalue in Complex and Real Correlated Wishart Ensembles
Mathematical Physics
2014-04-14 v2 math.MP
Statistics Theory
Statistics Theory
Abstract
For the correlated Gaussian Wishart ensemble we compute the distribution of the smallest eigenvalue and a related gap probability.We obtain exact results for the complex (\beta=2) and for the real case (\beta=1). For a particular set of empirical correlation matrices we find universality in the spectral density, for both real and complex ensembles and all kinds of rectangularity. We calculate the asymptotic and universal results for the gap probability and the distribution of the smallest eigenvalue. We use the Supersymmetry method, in particular the generalized Hubbard-Stratonovich transformation and superbosonization.
Keywords
Cite
@article{arxiv.1310.2467,
title = {Distribution of the Smallest Eigenvalue in Complex and Real Correlated Wishart Ensembles},
author = {Tim Wirtz and Thomas Guhr},
journal= {arXiv preprint arXiv:1310.2467},
year = {2014}
}
Comments
30 pages, 2 figures, improving pictures, correcting typos