  We demonstrate theoretically the spontaneous formation of a stochastic
polarization in exciton-polariton Bose-Einstein condensates in planar
microcavities under pulsed excitation. Below the threshold pumping intensity
(dependent on the polariton life-time) the average polarization degree is close
to zero, whilst above threshold the condensate acquires a polarization
described by a (pseudospin) vector with random orientation, in general. We
establish the link between second order coherence of the polariton condensate
and the distribution function of its polarization. We examine also the
mechanisms of polarization dephasing and relaxation.
