Sticky central limit theorems at isolated hyperbolic planar singularities


Journal Article

© 2015, University of Washington. Akll rights reserved. We derive the limiting distribution of the barycenter bn of an i.i.d. sample of n random points on a planar cone with angular spread larger than 2π. There are three mutually exclusive possibilities: (i) (fully sticky case) after a finite random time the barycenter is almost surely at the origin; (ii) (partly sticky case) the limiting distribution of √nbn comprises a point mass at the origin, an open sector of a Gaussian, and the projection of a Gaussian to the sector’s bounding rays; or (iii) (nonsticky case) the barycenter stays away from the origin and the renormalized fluctuations have a fully supported limit distribution—usually Gaussian but not always. We conclude with an alternative, topological definition of stickiness that generalizes readily to measures on general metric spaces.

Full Text

Duke Authors

Cited Authors

  • Huckemann, S; Mattingly, JC; Miller, E; Nolen, J

Published Date

  • January 1, 2015

Published In

Volume / Issue

  • 20 /

Electronic International Standard Serial Number (EISSN)

  • 1083-6489

Digital Object Identifier (DOI)

  • 10.1214/EJP.v20-3887

Citation Source

  • Scopus