Collective Online Clicking Pattern on BBS as Geometric Brown Motion

Abstract

In this paper, we focus on massive clicking pattern on BBS. We find that the frequency of clicking volumes on BBS satisfies log-normal distribution, and both the lower-tail and upper-tail demonstrate power-law pattern. According to the empirical statistical results, we find the collective attention on BBS is subject to exponential law instead of inversely proportional to time as suggested for Twitter [4]. Furthermore we link the dynamical clicking pattern to Geometric Brown Motion (GBM), rigorously prove that GBM observed after an exponentially distributed attention time will exhibit power law. Our endeavors in this study provide rigorous proof that log-normal, Pareto distributions, power-law pattern are unified, most importantly this result suggests that dynamic collective online clicking pattern might be governed by Geometric Brown Motion, embodied through log-normal distribution, even caused by different collective attention mechanisms.