Logarithmic scaling and stochastic criticality in collective attention
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911383799463936 |
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| author | Okamura, Keisuke |
| author_facet | Okamura, Keisuke |
| contents | We uncover a universal scaling law governing the dispersion of collective attention and identify its underlying stochastic criticality. By analysing large-scale ensembles of Wikipedia page views, we find that the variance of logarithmic attention grows ultraslowly, $\operatorname{Var}[\ln{X(t)}]\propto\ln{t}$, in sharp contrast to the power-law scaling typically expected for diffusive processes. We show that this behaviour is captured by a minimal stochastic differential equation driven by fractional Brownian motion, in which long-range memory ($H$) and temporal decay of volatility ($η$) enter through the single exponent $ξ\equiv H-η$. At marginality, $ξ=0$, the variance grows logarithmically, marking the critical boundary between power-law growth ($ξ>0$) and saturation ($ξ<0$). By incorporating article-level heterogeneity through a Gaussian mixture model, we further reconstruct the empirical distribution of cumulative attention within the same framework. Our results place collective attention in a distinct class of non-Markovian stochastic processes, with close affinity to ageing-like and ultraslow dynamics in glassy systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_12306 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Logarithmic scaling and stochastic criticality in collective attention Okamura, Keisuke Physics and Society Statistical Mechanics Digital Libraries Social and Information Networks Data Analysis, Statistics and Probability We uncover a universal scaling law governing the dispersion of collective attention and identify its underlying stochastic criticality. By analysing large-scale ensembles of Wikipedia page views, we find that the variance of logarithmic attention grows ultraslowly, $\operatorname{Var}[\ln{X(t)}]\propto\ln{t}$, in sharp contrast to the power-law scaling typically expected for diffusive processes. We show that this behaviour is captured by a minimal stochastic differential equation driven by fractional Brownian motion, in which long-range memory ($H$) and temporal decay of volatility ($η$) enter through the single exponent $ξ\equiv H-η$. At marginality, $ξ=0$, the variance grows logarithmically, marking the critical boundary between power-law growth ($ξ>0$) and saturation ($ξ<0$). By incorporating article-level heterogeneity through a Gaussian mixture model, we further reconstruct the empirical distribution of cumulative attention within the same framework. Our results place collective attention in a distinct class of non-Markovian stochastic processes, with close affinity to ageing-like and ultraslow dynamics in glassy systems. |
| title | Logarithmic scaling and stochastic criticality in collective attention |
| topic | Physics and Society Statistical Mechanics Digital Libraries Social and Information Networks Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2601.12306 |