Index distribution of the Ginibre ensemble

  title={Index distribution of the Ginibre ensemble},
  author={Romain Allez and J. Touboul and G. Wainrib},
  journal={Journal of Physics A},
  • Romain Allez, J. Touboul, G. Wainrib
  • Published 2014
  • Physics, Mathematics
  • Journal of Physics A
  • Complex systems, and in particular random neural networks, are often described by randomly interacting dynamical systems with no specific symmetry. In that context, characterizing the number of relevant directions necessitates fine estimates on the Ginibre ensemble. In this Letter, we compute analytically the probability distribution of the number of eigenvalues $N_R$ with modulus greater than $R$ (the index) of a large $N\times N$ random matrix in the real or complex Ginibre ensemble. We show… CONTINUE READING
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