Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sticky central limit theorems on open books   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 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).

28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin