  The propagation of an initially localized perturbation via an interacting
many-particle Hamiltonian dynamics is investigated. We argue that the
propagation of the perturbation can be captured by the use of a continuous-time
random walk where a single particle is traveling through an active, fluctuating
medium. Employing two archetype ergodic many-particle systems, namely (i) a
hard-point gas composed of two unequal masses and (ii) a Fermi-Pasta-Ulam chain
we demonstrate that the corresponding perturbation profiles coincide with the
diffusion profiles of the single-particle L\'{e}vy walk approach. The
parameters of the random walk can be related through elementary algebraic
expressions to the physical parameters of the corresponding test many-body
systems.
