  The appropriate selection of recurrence thresholds is a key problem in
applications of recurrence quantification analysis (RQA) and related methods
across disciplines. Here, we discuss the distribution of pairwise distances
between state vectors in the studied system's state space reconstructed by
means of time-delay embedding as the key characteristic that should guide the
corresponding choice for obtaining an adequate resolution of a recurrence plot.
Specifically, we present an empirical description of the distance distribution,
focusing on characteristic changes of its shape with increasing embedding
dimension. Based on our results, we recommend selecting the recurrence
threshold adaptively according to a fixed quantile of this distribution. We
highlight the advantages of this strategy over other previously suggested
approaches by discussing the performance of selected RQA measures in detecting
chaos--chaos transitions in some prototypical model system.
