Sticky central limit theorems on open books
Abstract
Given a probability distribution on an open book (a metric space obtained by gluing
a disjoint union of copies of a half-space along their boundary hyperplanes), we define
a precise concept of when the Fréchet mean (barycenter) is sticky. This nonclassical
phenomenon is quantified by a law of large numbers (LLN) stating that the empirical
mean eventually almost surely lies on the (codimension 1 and hence measure 0) spine
that is the glued hyperplane, and a central limit theorem (CLT) stating that the limiting
distribution is Gaussian and supported on the spine.We also state versions of the
LLN and CLT for the cases where the mean is nonsticky (i.e., not lying on the spine)
and partly sticky (i.e., is, on the spine but not sticky). © Institute of Mathematical
Statistics, 2013.
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Journal articlePermalink
https://hdl.handle.net/10161/9519Published Version (Please cite this version)
10.1214/12-AAP899Publication Info
(2013). Sticky central limit theorems on open books. Annals of Applied Probability, 23(6). pp. 2238-2258. 10.1214/12-AAP899. Retrieved from https://hdl.handle.net/10161/9519.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Jonathan Christopher Mattingly
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
Ezra Miller
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
James H. Nolen
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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