  We investigate the statistics of microcavity polariton Bose-Einstein
condensation by measuring photoluminescence dynamics from a GaAs microcavity
excited by single laser excitation pulses. We directly observe fluctuations
(jitter) of the polariton condensation onset time and model them using a master
equation for the occupancy probabilities. The jitter of the condensation onset
time is an inherent property of the condensate formation and its magnitude is
approximately equal to the rise time of the condensate density. We investigate
temporal correlations between the emission of condensate in opposite circular
or linear polarizations by measuring the second-order correlation function
$g^{(2)}(t_1,t_2)$. Polariton condensation is accompanied by spontaneous
symmetry breaking revealed by the occurrence of random (i.e., varying from
pulse to pulse) circular and linear polarizations of the condensate emission.
The degree of circular polarization generally changes its sign in the course of
condensate decay, in contrast to the degree of linear polarization.
