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  • 标题:The Intrinsic geometry of some random manifolds
  • 本地全文:下载
  • 作者:Sunder Ram Krishnan ; Jonathan E. Taylor ; Robert J. Adler
  • 期刊名称:Electronic Communications in Probability
  • 印刷版ISSN:1083-589X
  • 出版年度:2017
  • 卷号:22
  • DOI:10.1214/16-ECP4763
  • 语种:English
  • 出版社:Electronic Communications in Probability
  • 摘要: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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