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2015 Sticky central limit theorems at isolated hyperbolic planar singularities
Stephan Huckemann, Jonathan Mattingly, Ezra Miller, James Nolen
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Electron. J. Probab. 20: 1-34 (2015). DOI: 10.1214/EJP.v20-3887


We derive the limiting distribution of the barycenter $b_n$ of an i.i.d. sample of $n$ random points on a planar cone with angular spread larger than $2\pi$. 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 $\sqrt{n} b_n$ 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.


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Stephan Huckemann. Jonathan Mattingly. Ezra Miller. James Nolen. "Sticky central limit theorems at isolated hyperbolic planar singularities." Electron. J. Probab. 20 1 - 34, 2015.


Accepted: 21 July 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1327.60028
MathSciNet: MR3371437
Digital Object Identifier: 10.1214/EJP.v20-3887

Primary: 60B99
Secondary: 60F05


Vol.20 • 2015
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