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Index distribution of the Ginibre ensemble. (English) Zbl 1290.82024
The paper presents some results related to randomly interacting dynamical systems, estimates on the Ginibre ensemble, index around fixed points of discrete-time random dynamical systems and relevant physical models. The authors indicate a method to compute the probability distribution of the number of eigenvalues with modulus greater than the index of a large random matrix in a real or in a complex Ginibre ensemble and obtains explicit formula for the equilibrium spectral densities and the rate function.

MSC:
82C32 Neural nets applied to problems in time-dependent statistical mechanics
15B52 Random matrices (algebraic aspects)
92B20 Neural networks for/in biological studies, artificial life and related topics
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