The stability–complexity relationship at age 40: a random matrix perspective

@article{Allesina2014TheSR,
  title={The stability–complexity relationship at age 40: a random matrix perspective},
  author={Stefano Allesina and Si Hui Tang},
  journal={Population Ecology},
  year={2014},
  volume={57},
  pages={63-75}
}
Since the work of Robert May in 1972, the local asymptotic stability of large ecological systems has been a focus of theoretical ecology. Here we review May’s work in the light of random matrix theory, the field of mathematics devoted to the study of large matrices whose coefficients are randomly sampled from distributions with given characteristics. We show how May’s celebrated “stability criterion” can be derived using random matrix theory, and how extensions of the so-called circular law for… CONTINUE READING
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