Eigenvalue spectra of large correlated random matrices.
basic_science · Level V
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- Record sourced from PubMed, PMID 27967175.
- Also identified by PMC identifier 5161118.
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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.