  We consider the long-ranged Ising spin-glass with random couplings decaying
as a power-law of the distance, in the region of parameters where the
spin-glass phase exists with a positive droplet exponent. For the Metropolis
single-spin-flip dynamics near zero temperature, we construct via real-space
renormalization the full hierarchy of relaxation times of the master equation
for any given realization of the random couplings. We then analyze the
probability distribution of dynamical barriers as a function of the spatial
scale. This real-space renormalization procedure represents a simple explicit
example of the droplet scaling theory, where the convergence towards local
equilibrium on larger and larger scales is governed by a strong hierarchy of
activated dynamical processes, with valleys within valleys.
