
Publications [#243877] of Jonathan C. Mattingly
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 Hotz, T; Huckemann, S; Le, H; Marron, JS; Mattingly, JC; Miller, E; Nolen, J; Owen, M; Patrangenaru, V; Skwerer, S, Sticky central limit theorems on open books,
The Annals of Applied Probability, vol. 23 no. 6
(2013),
pp. 22382258, Institute of Mathematical Statistics, ISSN 10505164 [arXiv:1202.4267], [12AAP899], [doi]
(last updated on 2020/07/11)
Abstract: Given a probability distribution on an open book (a metric space obtained by gluing a disjoint union of copies of a halfspace along their boundary hyperplanes), we define a precise concept of when the Fr\'{e}chet 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).
