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arXiv · 2311.09385

Non-injectivity of Bures--Wasserstein barycentres in infinite dimensions

Yoav Zemel
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Abstract

We construct a counterexample to the injectivity conjecture of Masarotto et al (2018). Namely, we construct a class of examples of injective covariance operators on an infinite-dimensional separable Hilbert space for which the Bures--Wasserstein barycentre is highly non injective -- it has a kernel of infinite dimension.

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Yoav Zemel. 2023-11-15. Non-injectivity of Bures--Wasserstein barycentres in infinite dimensions. https://arxiv.org/abs/2311.09385

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