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arXiv · 1512.05622

The Intrinsic Geometry of Some Random Manifolds

Sunder Ram Krishnan·Jonathan E. Taylor·Robert J. Adler
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Abstract

We study the a.s. convergence of a sequence of random embeddings of a fixed manifold into Euclidean spaces of increasing dimensions. We show that the limit is deterministic. As a consequence, we show that many intrinsic functionals of the embedded manifolds also converge to deterministic limits. Particularly interesting examples of these functionals are given by the Lipschitz-Killing curvatures, for which we also prove unbiasedness, using the Gaussian kinematic formula.

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Sunder Ram Krishnan, Jonathan E. Taylor, Robert J. Adler. 2015-12-17. The Intrinsic Geometry of Some Random Manifolds. https://doi.org/10.1214/16-ecp4763

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