Isotropic Brownian motions over complex fields as a solvable model for May–Wigner stability analysis

@article{Ipsen2016IsotropicBM,
title={Isotropic Brownian motions over complex fields as a solvable model for May–Wigner stability analysis},
author={J. R. Ipsen and Henning Schomerus},
journal={Journal of Physics A: Mathematical and Theoretical},
year={2016},
volume={49}
}
• Published 20 February 2016
• Mathematics, Physics
• Journal of Physics A: Mathematical and Theoretical
We consider matrix-valued stochastic processes known as isotropic Brownian motions, and show that these can be solved exactly over complex fields. While these processes appear in a variety of questions in mathematical physics, our main motivation is their relation to a May–Wigner-like stability analysis, for which we obtain a stability phase diagram. The exact results establish the full joint probability distribution of the finite-time Lyapunov exponents, and may be used as a starting point for…
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