  In this paper we quantify the statistical properties and dynamics of the
frequency of hashtag use on Twitter. Hashtags are special words used in social
media to attract attention and to organize content. Looking at the collection
of all hashtags used in a period of time, we identify the scaling laws
underpinning the hashtag frequency distribution (Zipf's law), the number of
unique hashtags as a function of sample size (Heaps' law), and the fluctuations
around expected values (Taylor's law). While these scaling laws appear to be
universal, in the sense that similar exponents are observed irrespective of
when the sample is gathered, the volume and nature of the hashtags depends
strongly on time, with the appearance of bursts at the minute scale, fat-tailed
noise, and long-range correlations. We quantify this dynamics by computing the
Jensen-Shannon divergence between hashtag distributions obtained $\tau$ times
apart and we find that the speed of change decays roughly as $1/\tau$. Our
findings are based on the analysis of 3.5 billion hashtags used between 2015
and 2016.
