Heavy-tails and world records

In honor of the upcoming olympics, I figured I’d write a post highlighting something that JK, Bert, and I came up with in the process of writing our book on heavy tails.

One of the topics that is interwoven throughout the book is a connection between “extremal processes” and heavy-tails. In case you’re not familiar with extremal processes, the idea is that the process evolves as the max/min of a sequence of random variables. So, for example,

\displaystyle M_n = \min\{X_1, \ldots, X_n\}.

Of course, the canonical example of such processes is the evolution of world records. So, it felt like a good time to post about them here…

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