Math @ Duke

Publications [#225248] of Jonathan C. Mattingly
Papers Submitted
 with Stephan Huckemann, Ezra Miller, James Nolen, Sticky central limit theorems at isolated hyperbolic planar singularities
(October, 2014) [arXiv:1410.6879]
(last updated on 2014/10/27)
Abstract: 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 n‾√bn 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 distributionusually 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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