Title: Extreme Value Statistics of Highly Correlated Gaussian Processes
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Abstract: Extreme value theory in probability is concerned with the distribution of extrema of stochastic processes. In cases where the variables are independent or weakly correlated, the theory is well established, dating back to the '20s. On the other hand, the search for universal features in the statistics of highly correlated variables is still in development.
This problem is at the heart of the study of random matrix theory, random polymers, and spin glasses, among other examples. The first part of this talk will present the general challenges of the problem, with an emphasis on spin glass models. In the second part, we will explore in more detail a specific model, branching Brownian motion, which, in many aspects, is a limit case where correlations have an effect on the statistics.