Statistics of Bipolar Representation of CMB maps
  Gaussianity of temperature fluctuations in the Cosmic Microwave
Background(CMB) implies that the statistical properties of the temperature
field can be completely characterized by its two point correlation function.
The two point correlation function can be expanded in full generality in the
bipolar spherical harmonic(BipoSH) basis. Looking for significant deviations
from zero for Bipolar Spherical Harmonic(BipoSH) Coefficients derived from
observed CMB maps forms the basis of the strategy used to detect isotropy
violation. In order to quantify "significant deviation" we need to understand
the distributions of these coefficients. We analytically evaluate the moments
and the distribution of the coefficients of expansion($A^{LM}_{l_1 l_2}$),
using characteristic function approach. We show that for BipoSH coefficients
with M=0 an analytical form for the moments up to any arbitrary order can be
derived. For the remaining BipoSH coefficients with $M\neq0$, the moments
derived using the characteristic function approach need to be supplemented with
a correction term. The correction term is found to be important particularly at
low multipoles. We provide a general prescription for calculating these
corrections, however we restrict the explicit calculations only up to kurtosis.
We confirm our results with measurements of BipoSH coefficients on numerically
simulated statistically isotropic CMB maps.
