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The intrinsic geometry of some random manifolds

Publication Type : Journal Article

Publisher : Electronic Communications in Probability

Source : Electronic Communications in Probability, vol. 22, no. 1, pp. 1–12, Jan. 2017.

Url : https://projecteuclid.org/journals/electronic-communications-in-probability/volume-22/issue-none/The-Intrinsic-geometry-of-some-random-manifolds/10.1214/16-ECP4763.full

Campus : Amritapuri

School : School of Computing

Department : Computer Science and Engineering

Year : 2017

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.

Cite this Research Publication : S. R. Krishnan, J. E. Taylor, and R. J. Adler, “The intrinsic geometry of some random manifolds,” Electronic Communications in Probability, vol. 22, no. 1, pp. 1–12, Jan. 2017

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