A generalization of random matrix theory and its application to statistical physics

Area of Science:

• Statistical analysis
• Time series analysis
• Random matrix theory

Background:

• Cross-correlations are crucial in empirical data analysis.
• Traditional methods often overlook auto-correlation's influence.
• Understanding statistical structures in multiple time series is complex.

Purpose of the Study:

• To develop a novel method for cross-correlation analysis.
• To generalize random matrix theory for empirical data.
• To account for auto-correlations in cross-correlation studies.

Main Methods:

• Generalizing random matrix theory.
• Introducing autoregressive random matrix theory (ARRMT).
• Analytical and numerical determination of auto-correlation effects on eigenvalue distribution.

Main Results:

• Developed ARRMT to incorporate auto-correlations.
• Demonstrated ARRMT's applicability with inflation and air pressure data.
• Quantified the impact of auto-correlations on correlation matrix eigenvalues.

Conclusions:

• ARRMT provides a robust framework for analyzing cross-correlations.
• The method enhances statistical insights from time series data.
• Applicable to diverse fields like economics and environmental science.