title: Eigenvalue spectra of large correlated random matrices.
abstract: Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each other. The analytical results are confirmed by numerical simulations. The results have implications for the dynamics of neural and other biological networks where plasticity induces correlations in the connection strengths within the network. We find that the presence of correlations can have a major impact on network stability.
authors.affiliation: Computational Neurobiology Laboratory, Salk Institute for Biological Studies, La Jolla, California 92037, USA and Department of Physics, University of California, San Diego, California 92161, USA.
authors.forename: Alexander
authors.initials: A
authors.lastname: Kuczala
authors.affiliation: Computational Neurobiology Laboratory, Salk Institute for Biological Studies, La Jolla, California 92037, USA and Department of Physics, University of California, San Diego, California 92161, USA.
authors.forename: Tatyana O
authors.initials: TO
authors.lastname: Sharpee