Allez, Romain; Touboul, Jonathan; Wainrib, Gilles Index distribution of the Ginibre ensemble. (English) Zbl 1290.82024 J. Phys. A, Math. Theor. 47, No. 4, Article ID 042001, 8 p. (2014). 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. Reviewer: Claudia Simionescu-Badea (Wien) Cited in 7 Documents 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 Keywords:random matrices; Ginibre ensembles; saddle point method; large deviation theory; 2D-Coulomb gas; constrained optimization PDF BibTeX XML Cite \textit{R. Allez} et al., J. Phys. A, Math. Theor. 47, No. 4, Article ID 042001, 8 p. (2014; Zbl 1290.82024) Full Text: DOI arXiv