4 papers
Central limit theorems for Fréchet means on stratified spaces
Jonathan C. Mattingly, Ezra Miller, Do Tran
Fréchet means of samples from a probability measure on any smoothly stratified metric space M with curvature bounded above are shown to satisfy a central limit theorem (CLT). T…
Geometry of measures on smoothly stratified metric spaces
Jonathan C. Mattingly, Ezra Miller, Do Tran
Any measure on a CAT(k) space M that is stratified as a finite union of manifolds and has local exponential maps near the Fréchet mean yields a continuous "tangential c…
Shadow geometry at singular points of CAT(k) spaces
Jonathan C. Mattingly, Ezra Miller, Do Tran
In any CAT(k) space M, the "shadow" of a tangent vector Z at a point p is the set vectors that form an angle of πor more with Z. Taking logarithm maps at points approaching p along…
A central limit theorem for random tangent fields on stratified spaces
Jonathan C. Mattingly, Ezra Miller, Do Tran
Variation of empirical Fréchet means on a metric space with curvature bounded above is encoded via random fields indexed by unit tangent vectors. A central limit theorem shows thes…