  This paper deals with the study of dependencies between two given events
modeled by point processes. In particular, we focus on the context of DNA to
detect favored or avoided distances between two given motifs along a genome
suggesting possible interactions at a molecular level. For this, we naturally
introduce a so-called reproduction function h that allows to quantify the
favored positions of the motifs and which is considered as the intensity of a
Poisson process. Our first interest is the estimation of this function h
assumed to be well localized. The estimator based on random thresholds achieves
an oracle inequality. Then, minimax properties of the estimator on Besov balls
are established. Some simulations are provided, allowing the calibration of
tuning parameters from a numerical point of view and proving the good practical
behavior of our procedure. Finally, our method is applied to the analysis of
the influence between gene occurrences along the E. coli genome and occurrences
of a motif known to be part of the major promoter sites for this bacterium.
