arXiv subjects

M. A. Korzeniowska

Publications and source records attributed to M. A. Korzeniowska.

2 recordsLinked to original sources

arXiv2025

Long-range correlations with finite-size effects from a superposition of uncorrelated pulses with power-law distributed durations

Long-range correlations manifested as power spectral density scaling $1/f^β$ for frequency $f$ and a range of exponents $β$ are investigated for a superposition of uncorrelated pulses with distributed durations $τ$. Closed-form expressions for the frequency power spectral density are derived for a one-sided exponential pulse function and several variants of bounded and unbounded power-law distributions of pulse durations ${P_τ(τ)\sim1/τ^α}$ with abrupt and smooth cutoffs. The asymptotic scaling relation $β=3-α$ is demonstrated for $1<α<3$ in the limit of an infinitely broad distribution $P_τ(τ)$. Logarithmic corrections to the frequency scaling are exposed at the boundaries of the long-range dependence regime, $β=0$ and $β=2$. Analytically demonstrated finite-size effects associated with distribution truncations are shown to reduce the frequency ranges of scale invariance by several decades. The regimes of validity of the $β=3-α$ relation are clarified.

cond-mat.stat-mech↗

arXiv2023

Apparent universality of $1/f$ spectra as an artifact of finite-size effects

Power spectral density scaling with frequency $f$ as $1/f^β$ and $β\approx 1$ is widely found in natural and socio-economic systems. Consequently, it has been suggested that such self-similar spectra reflect the universal dynamics of complex phenomena. Here, we show that for a superposition of uncorrelated pulses with a power-law distribution of duration times the estimated scaling exponents $\barβ$ depend on the system size. We derive a parametrized, closed-form expression for the power spectral density, and demonstrate that for $β\in [0,2]$ the estimated scaling exponents have a bias towards $\barβ=1$. For $β=0$ and $β=2$ the explicit logarithmic corrections to frequency scaling are derived. The bias is particularly strong when the scale invariance spans less than four decades in frequency. Since this is the case for the majority of empirical data, the boundedness of systems well described by the superposition of uncorrelated pulses may contribute to overemphasizing the universality of $1/f$.

physics.data-an↗