  The statistics of records in sequences of independent, identically
distributed random variables is a classic subject of study. One of the earliest
results concerns the stochastic independence of record events. Recently,
records statistics beyond the case of i.i.d. random variables have received
much attention, but the question of independence of record events has not been
addressed systematically. In this paper, we study this question in detail for
the case of independent, non-identically distributed random variables,
specifically, for random variables with a linearly moving mean. We find a rich
pattern of positive and negative correlations, and show how their asymptotics
is determined by the universality classes of extreme value statistics.
