Extreme value theory

Extreme value theory (EVT) deals with the statistics of the largest or smallest values of a probability distribution, typically either in terms of block maxima or peak-over-thresholds. Just as in the case of the sum of random variables, “central limit” theorems exist for extremes, with some results even generalisable to correlated variables.

Aside from the intense study of EVT in time series, there is a surprisingly diverse range of open problems across the sciences, such as the energy levels of low-lying states in statistical physics, the spectrum of extreme eigenvalues in random matrices in mathematical physics, worst-case running times in computer science, DNA replication times in cell biology, and the pricing of life insurance policies in actuarial science, to name just a few.