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2017 The Intrinsic geometry of some random manifolds
Sunder Ram Krishnan, Jonathan E. Taylor, Robert J. Adler
Electron. Commun. Probab. 22: 1-12 (2017). DOI: 10.1214/16-ECP4763

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. "The Intrinsic geometry of some random manifolds." Electron. Commun. Probab. 22 1 - 12, 2017. https://doi.org/10.1214/16-ECP4763

Information

Received: 16 December 2015; Accepted: 25 November 2016; Published: 2017
First available in Project Euclid: 5 January 2017

zbMATH: 1366.57012
MathSciNet: MR3607796
Digital Object Identifier: 10.1214/16-ECP4763

Subjects:
Primary: 57N35, 60D05, 60G15
Secondary: 60G60, 70G45

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