Illustration of the correlations between events produced with the ReDecay method, using $N_{\text{ReDecay}}=100$: (left) autocorrelation function $R(\tau)$ for different values of the ratios of widths of the probability density functions, $\sigma_2/\sigma_1$ and (right) comparison of normalised distributions of a variable $x$ generated with the ReDecay method and a standard generation method (nominal) for $\sigma_1=5$ and $\sigma_2=1$. The bottom part of the right plot shows the pull distribution of the difference $\Delta$ in each bin of the distribution of the value obtained with the ReDecay method with the value from the nominal method, divided by the naive expectation for the statistical undertainty, $\sigma = \sqrt{N}$ where $N$ is the number of events in the bins. A unit Gaussian distribution is overlaid with the pull distribution to visualize their disagreement. The pull distribution has a width of $1.75\pm0.09$ indicating that uncertainties are underestimated in this illustration case.

Comparison of a ReDecay sample with a nominally produced sample of $ D ^0 \rightarrow K ^- K ^+ \pi ^+ \pi ^- $ decays. Shown are the invariant mass squared of the kaon pair (left) and pion pair (right) which are both independent of the kinematics of the decaying particle. Displayed uncertainties are computed assuming independent events. There is no sign of the effects caused by correlated events as seen in \cref{fig:illustration} (right).

Animated gif made out of all figures.