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.
Citation
Sunder Ram Krishnan. Jonathan E. Taylor. Robert J. Adler. "The Intrinsic geometry of some random manifolds." Electron. Commun. Probab. 22 1 - 12, 2017. https://doi.org/10.1214/16-ECP4763
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