What type of study is this?

This is a Quantitative Study study.

September 21, 2025

Convergence of Cones of Metric Measure Spaces and Its Application to Cauchy Distribution

SESyota EsakiOita University DKDaisuke KazukawaTokyo Metropolitan University AMAyato MitsuishiFukuoka University

Key Points

A sequence of cones in metric measure spaces converges under specific topologies.
The Cauchy distribution converges to a half line in concentration topology as dimensions grow.
This convergence presents a novel case apart from Gaussian distributions.
The findings enhance our understanding of metric measure spaces and statistical distributions.

Abstract

Abstract We prove that a sequence of cones of metric measure spaces converges if the sequence of the base spaces converges in Gromov’s box, concentration, and weak topologies. As an application, we show that the generalized Cauchy distribution with suitable scaling converges to a half line in the concentration topology as the dimension diverges to infinity. This is a new example distinguished from previously known examples such as Gaussian distributions and typical closed Riemannian manifolds with constant Ricci curvature.

KI fragen

Bookmark

View Full Paper