An Overview of Extreme Value Statistics
Much of our information about the world is reported in terms of statistical averages. Such averaged quantities are particularly meaningful when the deviations around the mean are negligible. In some processes, however, extreme deviations may dominate the statistics of the system. Moreover, extreme statistics are interesting in their own right: construction of flood levees (how high should one build?), stock price fluctuations (how to estimate Value at Risk?), surface corrosion (how long does a protective layer of paint last?).
After briefly describing how extremes are interpreted across disciplines, I will present a number of examples from physics in which the presence of correlations complicates matters considerably.