Riemannian barycentres: from harmonic maps and statistical shape to the classical central limit theorem
Wilfrid Kendall (May 25, 2012)
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The subject of Riemannian barycentres has a strikingly long history, stretching back to work of Frechet and Cartan. The first part of this talk will be a review of the fundamental ideas and a discussion of the work of various probabilists and statisticians on applications of the concept to probabilistic approaches to harmonic map theory and statistical shape theory. I will then present some recent joint work with Huiling Le concerning central limit theory for empirical barycentres, which to our considerable surprise has led us to a new perspective on the classical Lindeberg-Feller central limit theorem.