  The record statistics of complex random states are analytically calculated,
and shown that the probability of a record intensity is a Bernoulli process.
The correlation due to normalization leads to a probability distribution of the
records that is non-universal but tends to the Gumbel distribution
asymptotically. The quantum standard map is used to study these statistics for
the effect of correlations apart from normalization. It is seen that in the
mixed phase space regime the number of intensity records is a power law in the
dimensionality of the state as opposed to the logarithmic growth for random
states.
