The development of statistical analysis methods for the study of correlations and statistical memory effects in the recorded data of physical experiments

Abstract

In this paper, we discuss the prospects for the use of statistical analysis methods in the study of correlations and statistical memory effects in the experimental data of physical experiments. Developed methods under consideration: Memory Functions Formalism and Flicker-Noise Spectroscopy allow obtaining a large set of quantitative parameters and qualitative characteristics directly from temporal signals generated by complex physical systems. Additionally, for the study of collective phenomena and effects, one- and two-parameter cross-correlation functions are proposed, which allow studying cross-correlations between simultaneously recorded signals in spatially separated areas of the object under study. The introduced analytical relations and numerical algorithms can be applied to solve the problems of metrology of surface structures at the nano- and microlevels, to study collective phenomena in the plasma of astrophysical objects, the structure of molecules, and their complexes.