Correlation and autocorrelation is something that in my Bachelor's programme in physics has been somewhat overlooked, so I'm in trouble understanding their use in this paper (The prisoner’s dilemma on co-evolving networks under perfect rationality. C Bielya, K Dragositsa and S Thurnera. Physica D 228, 40-48, arXiv:physics/0504190 [physics.soc-ph]).
Basically, they have a dynamic network which shows periodic behaviour. They try to measure the degree distribution $P(k)$, but of course they have to average over time. So, they present the resulting $\langle P(k)\rangle$, specifying the following:
To improve the accuracy of the plot, degree distributions of networks at $10^3$ different times have been averaged. The correlation in the time series has been taken care of by using time intervals of inverse correlation length.
As I understand it, they want to avoid taking samples of the observable of interest at time intervals equal the period of the cyclic evolution of the system, because that would bias the result, based on when in the period you start sampling. If so, then I don't understand why taking the inverse of the correlation length is the preferred option.