I will discuss three disparate examples of evolving complex systems where the
notions of broad-tail distributions and extreme-value statistics play a
central role: (a) scientific citations, (b) record temperature events, and
(c) baseball statistics.
(a) After a brief presentation of empirical facts about citations, I will present the Google PageRank algorithm and apply it to the citation network to help uncover semi-forgotten scientific "gems".
(b) Using extreme statistics, I derive the expected number and the magnitude of record temperature events in a stationary climate. The effect of global warming on record temperature events is then considered. The current global warming rate measurably increases the frequency of temperature records compared to the case of a stationary climate.
(c) Finally, I apply a simple competition model that incorporates heterogeneity of team strengths to quantify team win/loss records as a function of their rank in major-league baseball over the past century. This same model also gives the distribution of team winning and losing streaks. Long streaks appear to have a primarily statistical origin. The data further show that baseball is becoming more competitive.