  We propose that fast scrambling on finite-entropy stretched horizons can be
modeled by a diffusion process on an effective ultrametric geometry. A
scrambling time scaling logarithmically with the entropy is obtained when the
elementary transition rates saturate causality bounds on the stretched horizon.
The so-defined ultrametric diffusion becomes unstable in the infinite-entropy
limit. A formally regularized version can be shown to follow a particular case
of the Kohlrausch law.
