  We clarify the structure of thermal noise in AdS/CFT by studying the dynamics
of an equilibrated heavy quark string. Using the Kruskal extension of the
correspondence to generate the dynamics of the field theory on the Keldysh
contour, we show that the motion of the string is described by the classical
equations of motion with a stochastic boundary condition on the stretched
horizon. The form of the stochastic boundary condition is consistent with the
dissipation on this surface and is found by integrating out the fluctuations
inside of the stretched horizon. Solving the equations of motion for the
fluctuating string we determine the full frequency dependence of the random
force on the boundary quark and show that it is consistent with the frequency
dependent dissipation. We show further that the stochastic motion reproduces
the bulk to bulk two point functions of the Kruskal formalism. These turn out
to be related to the usual retarded bulk to bulk propagator by KMS relations.
Finally we analyze the stochastic equations and give a bulk picture of the
random boundary force as a flip-flopping trailing string solution. The basic
formalism can be applied to the fluctuations of gravitons, dilatons, and other
fields.
