Fractional stochastic model of citation dynamics with memory and volatility
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908588377636864 |
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| author | Okamura, Keisuke |
| author_facet | Okamura, Keisuke |
| contents | Understanding the statistical laws governing citation dynamics remains a fundamental challenge in network theory and the science of science. Citation networks typically exhibit in-degree distributions well approximated by log-normal distributions yet also display power-law behaviour in the high-citation regime -- an apparent contradiction lacking a unified explanation. Here we identify a previously unrecognised phenomenon: the variance of the logarithm of citation counts per unit time follows a power law with respect to time ($t$) since publication, scaling as $t^{H}$, with $H$ constant. This discovery introduces a new challenge while simultaneously offering a crucial clue to resolving this discrepancy. We develop a stochastic model in which latent attention to publications evolves through a memory-driven process with cumulative advantage, modelled as fractional Brownian motion with Hurst parameter $H$ and volatility. We show that antipersistent fluctuations in attention ($H < 1/2$) yield log-normal citation distributions, whereas persistent attention dynamics ($H > 1/2$) favour heavy-tailed power laws, thus resolving the log-normal--power-law contradiction. Numerical simulations confirm both the $t^{H}$ law and the transition between regimes. Empirical analysis of arXiv e-prints indicates that the latent attention process is intrinsically antipersistent ($H \approx 0.13$). By linking memory effects and stochastic fluctuations in attention to broader network dynamics, our findings provide a unifying framework for understanding the evolution of collective attention in science and other attention-driven processes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_03011 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional stochastic model of citation dynamics with memory and volatility Okamura, Keisuke Physics and Society Statistical Mechanics Digital Libraries Social and Information Networks Understanding the statistical laws governing citation dynamics remains a fundamental challenge in network theory and the science of science. Citation networks typically exhibit in-degree distributions well approximated by log-normal distributions yet also display power-law behaviour in the high-citation regime -- an apparent contradiction lacking a unified explanation. Here we identify a previously unrecognised phenomenon: the variance of the logarithm of citation counts per unit time follows a power law with respect to time ($t$) since publication, scaling as $t^{H}$, with $H$ constant. This discovery introduces a new challenge while simultaneously offering a crucial clue to resolving this discrepancy. We develop a stochastic model in which latent attention to publications evolves through a memory-driven process with cumulative advantage, modelled as fractional Brownian motion with Hurst parameter $H$ and volatility. We show that antipersistent fluctuations in attention ($H < 1/2$) yield log-normal citation distributions, whereas persistent attention dynamics ($H > 1/2$) favour heavy-tailed power laws, thus resolving the log-normal--power-law contradiction. Numerical simulations confirm both the $t^{H}$ law and the transition between regimes. Empirical analysis of arXiv e-prints indicates that the latent attention process is intrinsically antipersistent ($H \approx 0.13$). By linking memory effects and stochastic fluctuations in attention to broader network dynamics, our findings provide a unifying framework for understanding the evolution of collective attention in science and other attention-driven processes. |
| title | Fractional stochastic model of citation dynamics with memory and volatility |
| topic | Physics and Society Statistical Mechanics Digital Libraries Social and Information Networks |
| url | https://arxiv.org/abs/2503.03011 |