Title: Large deviation principle for persistence diagrams of random cubical filtrations
Speaker: Shu Kanazawa (Kyoto University)
Abstract: The objective of this work is to investigate the asymptotic behavior of the persistence diagrams of a random cubical filtration as the window size tends to infinity. Here, a random cubical filtration is an increasing family of random cubical sets, which are the union of randomly generated higher dimensional unit cubes with integer coordinates in a Euclidean space. We first prove the strong law of large numbers for the persistence diagrams, inspired by the work of Hiraoka, Shirai, and Trinh. In this talk, we are mainly interested in the decay rate of the probability that the persistence diagram is far from the limiting measure. This is the first result on the large deviation behavior of persistence diagrams themselves. This talk is based on joint work with Yasuaki Hiraoka, Jun Miyanaga, and Kenkichi Tsunoda.
URL associated with Seminar: https://tgda.osu.edu/activities/tdga-seminar/
