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math.PR2023★ 2 cited
Large Sample Theory for Bures-Wasserstein Barycentres
Leonardo V. Santoro, Victor M. Panaretos
We establish a strong law of large numbers and a central limit theorem in the Bures-Wasserstein space of covariance operators -- or equivalently centred Gaussian measures -- over a…
math.PR2023
A Karhunen-Loève Theorem for Random Flows in Hilbert spaces
Leonardo V. Santoro, Kartik G. Waghmare, Victor M. Panaretos
We develop a generalisation of Mercer's theorem to operator-valued kernels in infinite dimensional Hilbert spaces. We then apply our result to deduce a Karhunen-Loève theorem, vali…