Concerning the statistics of cosmic magnetism
  Magnetic fields appear to be a generic feature of the early universe and are
a natural source of secondary CMB non-Gaussianity. In recent years the
statistical nature of the stresses of a primordial magnetic field has been well
studied. In this paper we confirm and extend these studies at one- and
two-point level, and present analytical results for a wide range of power-law
spectra. We also consider two non-power law cases of interest: a blue spectrum
with an extended damping tail on small scales, which could be generated by the
non-linear mixing of density and vorticity; and a red spectrum with a damping
tail on large scales. We then briefly consider the CMB impacts that result from
such fields. While this paper focuses on the one- and two-point moments, the
techniques we employ are designed to ease the analysis of the full bispectra
induced by primordial magnetic fields.
