  The effective theory for the dynamics of hot non-Abelian gauge fields with
spatial momenta of order of the magnetic screening scale g^2 T is described by
a Boltzmann equation. The dynamical content of this theory is explored. There
are three relevant frequency scales, g T, g^2 T and g^4 T, associated with
plasmon oscillations, multipole fluctuations of color charge, and with the
non-perturbative gauge field dynamics, respectively. The frequency scale g T is
integrated out. The result is a local Langevin-type equation. It is valid to
leading order in g and to all orders in log(1/g), and it does not suffer from
the hard thermal loop divergences of classical thermal Yang-Mills theory. We
then derive the corresponding Fokker-Planck equation, which is shown to
generate an equilibrium distribution corresponding to 3-dimensional Yang-Mills
theory plus a Gaussian free field.
