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Economic and ecological models can be extremely complex, with a large numberof agents/species each featuring multiple dynamical quantities. In an attemptto understand the generic stability properties of such systems, we define andstudy an interesting new matrix ensemble with extensive correlations. We findanalytically the boundary of its eigenvalue spectrum in the complex plane, as afunction of the correlations determined by the model at hand. We solvenumerically our equations in several cases of interest, and show that theresulting spectra can take a surprisingly wide variety of shapes.

The Stability Matrix Spectrum of Large Ecological and Economical Systems