The Intrinsic Geometry of Some Random Manifolds
Probability
2017-01-20 v1 Differential Geometry
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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Cite
@article{arxiv.1512.05622,
title = {The Intrinsic Geometry of Some Random Manifolds},
author = {Sunder Ram Krishnan and Jonathan E. Taylor and Robert J. Adler},
journal= {arXiv preprint arXiv:1512.05622},
year = {2017}
}
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11 pages