Universality for products of random matrices I: Ginibre and truncated unitary cases
arXiv:1411.2787
Abstract
Recently, the joint probability density functions of complex eigenvalues for products of independent complex Ginibre matrices have been explicitly derived as determinantal point processes. We express truncated series coming from the correlation kernels as multivariate integrals with singularity and investigate saddle point method for such a type of integrals. As an application, we prove that the eigenvalue correlation functions have the same scaling limits as those of the single complex Ginibre ensemble, both in the bulk and at the edge of the spectrum. We also prove that the similar results hold true for products of independent truncated unitary matrices.
41 pages; revised upon the suggestions of the anonymous referees; to appear in International Mathematics Research Notices. in IMRN 2015
References in corpus (5)
- Recent exact and asymptotic results for products of independent random matrices
- Weak Commutation Relations and Eigenvalue Statistics for Products of Rectangular Random Matrices
- On the Asymptotic Spectrum of Products of Independent Random Matrices
- Universal microscopic correlation functions for products of truncated unitary matrices
- Products of independent elliptic random matrices