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Two correlation patterns as indicators for underlying dynamics of complex systems.

Yuanfang Wu1, Lianshou Liu, Yingdan Wang

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This study introduces two spatial correlation patterns to measure random multiplicative cascade processes. These patterns effectively distinguish between correlated and uncorrelated events in high-energy physics.

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Area of Science:

  • High Energy Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Random multiplicative cascade processes are fundamental in various scientific fields.
  • Distinguishing between correlated and uncorrelated processes is crucial for understanding complex systems.
  • Existing methods may lack scale-independent measures for these processes.

Purpose of the Study:

  • To propose novel spatial correlation patterns for analyzing random multiplicative cascade processes.
  • To establish scale-independent and distinguishable measures for these processes.
  • To explore the applicability of these patterns in high-energy physics.

Main Methods:

  • Development of two spatial correlation patterns: fixed-to-arbitrary and neighboring bin correlations.
  • Demonstration of the scale-independent nature of these measures.
  • Validation of their ability to differentiate correlated from uncorrelated processes.

Main Results:

  • The proposed correlation patterns provide distinct and scale-independent metrics.
  • These patterns successfully characterize correlated and uncorrelated random multiplicative cascades.
  • The utility of these measures is shown in the context of relativistic heavy ion collisions.

Conclusions:

  • The novel spatial correlation patterns offer robust tools for analyzing cascade processes.
  • These methods enhance the understanding of correlations in complex systems.
  • The findings have direct implications for interpreting data from high-energy particle collisions.