STABILITY OF RANDOM-MATRIX MODELS

Random matrices have been widely studied as neutral models for the stability of large systems and, in particular, ecosystems. However, many ecologists interpret stability in terms of low variability and persistence, not Lyapunov stability studied in matrix theory. Following Harrison [5], Hastings [6] suggested a close relationship between Lyapunov stability and low variability for random matrix models with additional noise terms. We report on a simulation study confirming this conjecture and its extension to certain products of random matrices.