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math.ST2026
Expected number density of critical points of smooth Gaussian random fields in arbitrary dimensions
Satoshi Kuriki, Takahiko Matsubara, Satoshi Iso
We obtain explicit formulas for the expected number and height distribution of critical points of smooth isotropic Gaussian random fields on . The expected number den…
math.ST2025
Adversarially Robust Topological Inference
Siddharth Vishwanath, Bharath K. Sriperumbudur, Kenji Fukumizu +1
The distance function to a compact set plays a crucial role in the paradigm of topological data analysis. In particular, the sublevel sets of the distance function are used in the…
math.ST2024
Integrated empirical measures and generalizations of classical goodness-of-fit statistics
Hsien-Kuei Hwang, Satoshi Kuriki
Based on -fold integrated empirical measures, we study three new classes of goodness-of-fits tests, generalizing Anderson-Darling, Cramér-von Mises, and Watson statistics, resp…