  We study the propagation of waves in a medium in which the wave velocity
fluctuates randomly in time. We prove that at long times, the statistical
distribution of the wave energy becomes log-normal, with the average energy
growing exponentially with time. For weak disorder, another regime preexists at
shorter times, in which the energy follows a negative exponential distribution,
with an average value growing linearly with time. The theory is in perfect
agreement with numerical simulations, and applies to different kinds of waves.
The existence of such universal statistics bridges the fields of wave
propagation in time-disordered and space-disordered media.
