Bootstrapping cascaded random matrix models: Correlations in permutations of matrix products

Area of Science:

• Physics
• Wave Propagation
• Statistical Mechanics

Background:

• Random matrix theory is crucial for analyzing multiple scattering in disordered media.
• Simulating wave propagation through thick media requires cascading many random matrices, increasing computational load.
• Existing methods face computational challenges in modeling thick disordered systems.

Purpose of the Study:

• To propose a novel dual pool bootstrapping approach for accelerating statistical studies of scattering in thick random media.
• To investigate the impact of matrix reuse on statistical estimates of population averages.
• To analyze the bias and variance introduced by bootstrapping in these estimations.

Main Methods:

• Development of a dual pool based bootstrapping technique for random matrix analysis.
• Examination of potential matrix reuse within the bootstrapping framework.
• Analysis of bias and variance in sample mean estimators.

Main Results:

• The dual pool bootstrapping approach significantly speeds up statistical studies.
• Matrix reuse introduces bias and additional variance in the sample mean estimator.
• In the diffusive regime, extra variance arises from permuted matrix products, quantified through combinatorial analysis.

Conclusions:

• The proposed method offers an efficient alternative for studying wave scattering in thick disordered media.
• Understanding the statistical impact of matrix reuse is critical for accurate estimations.
• The findings provide a quantitative framework for analyzing correlations in scattering phenomena.