  We study the phenomenon of weak ergodicity breaking for a class of globally
correlated random walk dynamics defined over a finite set of states. The
persistence in a given state or the transition to another one depends on the
whole previous temporal history of the system. A set of waiting time
distributions, associated to each state, set the random times between
consecutive steps. Their mean value is finite for all states. The probability
density of time-averaged observables is obtained for different memory
mechanisms. This statistical object explicitly shows departures between time
and ensemble averages. While the mean residence time in each state may result
divergent, we demonstrate that this condition is in general not necessary for
breaking ergodicity. Hence, global memory effects are an alternative mechanism
able to induce this property. Analytical and numerical calculations support
these results.
