  We investigate the properties of the (complex) coefficients obtained in a
spherical harmonic representation of temperature maps of the cosmic microwave
background (CMB). We study the effect of the coefficient phase only, as well as
the combined effects of phase and amplitude. The method used to check for
anomalies is to construct a ``random walk'' trajectory in the complex plane
where the step length and direction are given by the amplitude and phase
(respectively) of the harmonic coefficient. If the fluctuations comprise a
homogeneous and isotropic Gaussian random field on the sky, the path so
obtained should be a classical ``Rayleigh flight'' with very well known
statistical properties. We illustrate the use of this random-walk
representation by using the net walk length as a test statistic, and apply the
method to the coefficients obtained from a Wilkinson Microwave Anisotropy Probe
(WMAP) preliminary sky temperature map.
