Long-range Clustering of Extremes
In this talk I will go over a few recent examples of stationary sequences, of which the extremes form long-range clustering. The phenomena of clustering of extremes have been extensively investigated in the literature since 1980s. However, for most examples the extremal clustering occurs only locally. That is, the locations of extremes within each cluster are bounded and shrink to a single point at the macroscopic level after normalization. For long-range clustering, on the other hand, the locations of extremes within each cluster are unbounded, and they can be further characterized by a random closed set in the scaling limit.
There are two classes of models that recently have been shown to exhibit the phenomena of long-range clustering of extremes. One is the Karlin model, which this talk will focus on. The other is the so-called stable-regenerative model, of which if time permits I will highlight briefly some key features.
Based on joint works with Olivier Durieu (Université de Tours, France) and Gennady Samorodnitsky (Cornell University, USA).
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