  We study a family of weighted random walks on complete graphs. These
`democratic walks' turn out to be explicitly solvable, and we find the
hierarchy window for which the characteristic time scale saturates the
so-called fast scrambling conjecture. We show that these democratic walks
describe well the properties of information spreading in systems in which every
degree of freedom interacts with every other degree of freedom, such as Matrix
or infinite range models. The argument is based on the analysis of suitably
defined `Information fields' ($\mathcal{I}$), which are shown to evolve
stochastically towards stationarity due to unitarity of the microscopic model.
The model implies that in democratic systems, stabilization of one subsystem is
equivalent to global scrambling. We use these results to study scrambling of
infalling perturbations in black hole backgrounds, and argue that the near
horizon running coupling constants are connected to entanglement evolution of
single particle perturbations in democratic systems.
