Math @ Duke

Publications [#243900] of Ezra Miller
Papers Published
 with 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, ISSN 10505164 [math.PR/1202.4267], [12AAP899], [doi]
(last updated on 2018/08/20)
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 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 (that is,
not lying on the spine) and partly sticky
(that is, on the spine but not sticky).


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