Correlation Integral vs. second order Factorial Moments and an efficient computational technique

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.

arXiv comment30 pages, 15 figures, accompanied by source program code in FORTRAN 90 (also in txt form). Revised version

References in corpus (9)

• Scaling laws for density correlations and fluctuations in multiparticle dynamics
• Critical Opalescence in Baryonic QCD Matter
• Pion production from a critical QCD phase
• Fractal Dimension Estimation with Persistent Homology: A Comparative Study
• Fractality in momentum space: a signal of criticality in nuclear collisions
• Local Multiplicity Fluctuations as a Signature of Critical Hadronization at LHC
• Observable Properties of Quark-Hadron Phase Transition at the Large Hadron Collider
• Evolutionary intermittency and the QCD critical point
• Ising-QCD phenomenology close to the critical point

Cited by in corpus (3)

• Energy Dependence of Intermittency for Charged Hadrons in Au+Au Collisions at RHIC
• Intermittency of charged particles in the hybrid UrQMD+CMC model at energies available at the BNL Relativistic Heavy Ion Collider
• A new approach to handling factorial moment correlations through principal component analysis