  The brightness temperature fluctuations in the 21 cm background related to
neutral Hydrogen distribution provide a probe of physics related to the era of
reionization when the intergalactic medium changed from a completely neutral to
a partially ionized one. We formulate statistics of 21 cm brightness
temperature anisotropies in terms of the angular power spectrum, the
bispectrum, and the trispectrum. Using the trispectrum, we estimate the
covariance related to the power spectrum measurements and show that
correlations resulting from non-Gaussianities are below a percent, at most.
While all-sky observations of the 21 cm background at arcminute-scale
resolution can be used to measure the bispectrum with a cumulative
signal-to-noise ratio of order a few ten, in the presence of foregrounds and
instrumental noise related to first-generation interferometers, the measurement
is unlikely to be feasible. For most purposes, non-Gaussianities in 21 cm
fluctuations can be ignored and the distribution can be described with Gaussian
statistics. Since 21 cm fluctuations are significantly contaminated by
foregrounds, such as galactic synchrotron or low-frequency radio point sources,
the lack of a significant non-Gaussianity in the signal suggests that any
significant detection of a non-Gaussianity can be due to foregrounds.
Similarly, in addition to frequency information that is now proposed to
separate 21 cm fluctuations from foregrounds, if the non-Gaussian structure of
foregrounds is a priori known, one can potentially use this additional
information to further reduce the confusion.
