Sticky central limit theorems at isolated hyperbolic planar singularities
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© 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.
Published Version (Please cite this version)10.1214/EJP.v20-3887
Publication InfoHuckemann, Stephan; Mattingly, Jonathan C; Miller, Ezra; & Nolen, James (2015). Sticky central limit theorems at isolated hyperbolic planar singularities. Electronic Journal of Probability, 20. 10.1214/EJP.v20-3887. Retrieved from https://hdl.handle.net/10161/9516.
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James B. Duke Distinguished Professor
Jonathan Christopher Mattingly grew up in Charlotte, NC where he attended Irwin Ave elementary and Charlotte Country Day. He graduated from the NC School of Science and Mathematics and received a BS is Applied Mathematics with a concentration in physics from Yale University. After two years abroad with a year spent at ENS Lyon studying nonlinear and statistical physics on a Rotary Fellowship, he returned to the US to attend Princeton University where he obtained a PhD in Applied and
Professor of Mathematics
Professor Miller's research centers around problems in geometry, algebra, topology, combinatorics, statistics, probability, and computation originating in mathematics and the sciences, including biology, chemistry, computer science, and imaging. The techniques range, for example, from abstract algebraic geometry or commutative algebra of ideals and varieties to concrete metric or discrete geometry of polyhedral spaces; from deep topological constructions such as equivariant K-theor
Professor of Mathematics
I study partial differential equations and probability, which have been used to model many phenomena in the natural sciences and engineering. In some cases, the parameters for a partial differential equation are known only approximately, or they may have fluctuations that are best described statistically. So, I am especially interested in differential equations modeling random phenomena and whether one can describe the statistical properties of solutions to these equations. Asymptotic anal
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