Logarithmic scaling and stochastic criticality in collective attention

Abstract: 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.