Averaging in random systems of nonnegative matrices

Janusz Mierczyński

Published 2014-08-10, updated 2015-04-09Version 2

It is proved that for the top Lyapunov exponent of a random matrix system of the form $\{A D(\omega)\}$, where $A$ is a nonnegative matrix and $D(\omega)$ is a diagonal matrix with positive diagonal entries, is bounded from below by the top Lyapunov exponent of the averaged system. This is in contrast to what one should expect of systems describing biological metapopulations.