Abstract
We develop a mapping between the factorial moments of the second order F_2 and the correlation integral C. We formulate a fast computation technique for the evaluation of both, which is more efficient, compared to conventional methods, for data containing number of pairs per event which is lower than the estimation points. We find the effectiveness of the technique to be more prominent as the dimension of the embedding space increases. We are able to analyse large amount of data in short computation time and access very low scales in C or extremely high partitions in F_2. The technique is an indispensable tool for detecting a very weak signal hidden in strong noise.
Highlights
Factorial moment analysis has been introduced in [1,2] as a very promising tool to study correlation phenomena in particle physics
We note that the correlation integral, which is connected to distances between pair of points, has been related here to the factorial moments of the second order, which, count pairs
We have developed a general mapping between correlation integral and second order scaled factorial moments which constitute two important tools used for the description of correlations in arbitrary data sets
Summary
Factorial moment analysis has been introduced in [1,2] as a very promising tool to study correlation phenomena in particle physics. It has been argued in several works [3–18] that long range correlations related to critical behaviour can be detected through the occurrence of powerlaw behaviour of the factorial moments as a function of the scale. In particle physics, this behaviour, called intermittency, is expected to occur at very small momentum differences as a manifestation of the phenomenon of critical opalescence [19]. In the present work we provide an alternative way to overcome this difficulty propos-
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