  A main characteristic of social media is that its diverse content, copiously
generated by both standard outlets and general users, constantly competes for
the scarce attention of large audiences. Out of this flood of information some
topics manage to get enough attention to become the most popular ones and thus
to be prominently displayed as trends. Equally important, some of these trends
persist long enough so as to shape part of the social agenda. How this happens
is the focus of this paper. By introducing a stochastic dynamical model that
takes into account the user's repeated involvement with given topics, we can
predict the distribution of trend durations as well as the thresholds in
popularity that lead to their emergence within social media. Detailed
measurements of datasets from Twitter confirm the validity of the model and its
predictions.
