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Sticky central limit theorems at isolated hyperbolic planar singularities

dc.contributor.author Huckemann, S
dc.contributor.author Mattingly, Jonathan Christopher
dc.contributor.author Miller, E
dc.contributor.author Nolen, James H
dc.date.accessioned 2015-03-20T17:51:14Z
dc.date.issued 2015-01-01
dc.identifier.uri http://hdl.handle.net/10161/9516
dc.description.abstract © 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 √nb<inf>n</inf> 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.
dc.relation.ispartof Electronic Journal of Probability
dc.relation.isversionof 10.1214/EJP.v20-3887
dc.title Sticky central limit theorems at isolated hyperbolic planar singularities
dc.type Journal article
pubs.organisational-group Duke
pubs.organisational-group Mathematics
pubs.organisational-group Statistical Science
pubs.organisational-group Trinity College of Arts & Sciences
pubs.publication-status Published
pubs.volume 20
dc.identifier.eissn 1083-6489


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