  Using the gauge/string duality, we derive a set of Langevin equations
describing the dynamics of a relativistic heavy quark moving with constant
average speed through the strongly-coupled N=4 SYM plasma at finite
temperature. We show that the stochasticity arises at the string world-sheet
horizon, and thus is causally disconnected from the black hole horizon in the
space-time metric. This hints at the non-thermal nature of the fluctuations, as
further supported by the fact that the noise term and the drag force in the
Langevin equations do not obey the Einstein relation. We propose a physical
picture for the dynamics of the heavy quark in which dissipation and
fluctuations are interpreted as medium-induced radiation and the associated
quantum-mechanical fluctuations. This picture provides the right parametric
estimates for the drag force and the (longitudinal and transverse) momentum
broadening coefficients.
