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Area of Science:

  • Statistical Mechanics
  • Time Series Analysis
  • Probability Theory

Background:

  • Classical large deviation theory quantifies outlier probabilities in time-averaged, independent, and identically distributed data.
  • Understanding deviations in correlated data is crucial for accurate statistical modeling.

Purpose of the Study:

  • Investigate large-deviation probabilities (LDPs) for time averages in Gaussian processes with short- and long-range correlations.
  • Examine the impact of intermittency on LDPs using a deterministic map.

Main Methods:

  • Analysis of large-deviation probabilities (LDPs) for time averages.
  • Studying Gaussian processes with varying correlation structures (short- and long-range).
  • Numerical illustration using a deterministic intermittent map.

Main Results:

  • Long-range correlations in Gaussian processes result in subexponential decay of LDPs.
  • A deterministic intermittent map generates long-range correlated time series.
  • Intermittency leads to a power law decay of LDPs, irrespective of correlation time finiteness.

Conclusions:

  • Long-range correlations fundamentally alter the decay rate of large deviation probabilities.
  • Intermittent dynamics provide a mechanism for power-law decay in LDPs, extending beyond standard statistical assumptions.