Speaker: Ray (Shuyang) Bai, University of Georgia.

Title: An Unusual Example of Extremal Clustering.

Abstract: Extreme value theory for stationary processes has been well developed over the past decades. Central to the theory is the notion of the extremal index, which quantifies the strength of clustering of extreme values due to dependence and appears as a correcting factor in the limit distribution. Classical theory provides a predictive formula for the extremal index, known as the candidate extremal index, which is typically equal to the extremal index under mild regularity conditions. In this talk, we introduce a double series model constructed via intersections of independent discrete renewal processes with infinite mean. This model exhibits an unusual phenomenon: the extremal index and the candidate extremal index differ. We further discuss several other surprising consequences that arise from this discrepancy. The talk is based on joint works with Rafal Kulik and Yizao Wang.