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Disordered beta thinned ensemble with applications.

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This summary is machine-generated.

Statistical spectral analysis reveals that disorder and incompleteness in random matrix theory (RMT) spectra cause quenched local statistics and fluctuating long-range statistics, following Taylor's law.

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Area of Science:

  • Physics
  • Complex Systems Analysis
  • Data Science

Background:

  • Statistical theories of spectra offer insights into Hamiltonian systems.
  • Analyzing spectra beyond traditional Hamiltonian levels requires advanced statistical methods.

Purpose of the Study:

  • To conduct a comprehensive spectral analysis measuring both local and long-range statistics.
  • To investigate the phenomenon of quenched local statistics alongside fluctuating long-range statistics.

Main Methods:

  • Combined three extensions of standard random matrix theory (RMT).
  • Analyzed long spectra incorporating disorder and level incompleteness.
  • Investigated fluctuation scaling (FS) and Taylor's law in spectral statistics.

Main Results:

  • Demonstrated that disorder and incompleteness in RMT spectra lead to quenched local and fluctuating long-range statistics.
  • Identified Taylor's law governing long-range statistics, indicating a fluctuation scaling mechanism.
  • Showcased applications in diverse fields like complex networks, COVID-19 time series, and linguistics.

Conclusions:

  • Short- and long-range spectral statistics reflect rigid and elastic characteristics, respectively.
  • The findings provide a framework for spectral data classification across various domains.
  • This approach deepens the understanding of spectral analysis beyond Hamiltonian systems.