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 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.

Ptolemaic Mummy Stuffings, 2: A Comic Fragment and Grammatical Text in the Yale Collection (P. CtYBR inv. 5019, 5043)

This is the second installment of a three-part project to publish a group of ten Ptolemaic papyri purchased by Yale’s Beinecke Library in 1998 (acquisition “1998b”), which came to the Beinecke as three hard wads that were apparently the stuffing from the stomach cavity of a mummified animal. This article publishes: (1) P.CtYBR inv. 5019, a fragment of line ends in iambic tetrameter catalectic meter from an unknown comedy; the format suggests that this is a further example of certain type of Ptolemaic writing exercise. (2) P.CtYBR inv. 5043, a fragmentary grammatical text of uncertain import.