Statistical analysis of 2D patterns and its application to astrometry

A general statistical procedure for analysis of finite 2D patterns, inspired by analysis of heavy-ion data, is developed. The method is verified in the study of publicly available data obtained by the Gaia-ESA mission. We prove that the procedure can be sensitive to the limits of accuracy of measurement, but it can also clearly identify the real physical effects on the large background of random distributions. As an example, the method confirms presence of binary and ternary star systems in the studied data. At the same time the possibility of statistical detection of gravitational microlensing effect is discussed.