# The Spectral Boundary of Block Structured Random Matrices

Journal of Physics: Complexity（2023）

Abstract

Economic and ecological models can be extremely complex, with a large number
of agents/species each featuring multiple interacting dynamical quantities. In
an attempt to understand the generic stability properties of such systems, we
define and study an interesting new matrix ensemble with extensive
correlations, generalising the elliptic ensemble. We determine analytically the
boundary of its eigenvalue spectrum in the complex plane, as a function of the
correlations determined by the model at hand. We solve numerically our
equations in several cases of interest, and show that the resulting spectra can
take a surprisingly wide variety of shapes.

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Key words

statistical physics,theoretical ecology,agent based models,random matrix theory

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