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Asymptotic Measures and Links in Simplicial Complexes

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Abstract

We introduce canonical measures on a locally finite simplicial complex K and study their asymptotic behavior under infinitely many barycentric subdivisions. We prove that the simplices of each dimension in \(\text {Sd}^d(K)\) equidistribute in |K| with respect to the Lebesgue measure as d grows to \(+\infty \) and then prove that their asymptotic link and dual block are universal.

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Acknowledgements

We are grateful to the referee for the suggestions to improve the paper.

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Authors and Affiliations

  1. Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, 69622, Villeurbanne Cedex, France

    Nermin Salepci & Jean-Yves Welschinger

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  1. Nermin Salepci
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  2. Jean-Yves Welschinger
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Correspondence to Nermin Salepci.

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The second author is partially supported by the ANR project MICROLOCAL (ANR-15CE40-0007-01).

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Salepci, N., Welschinger, JY. Asymptotic Measures and Links in Simplicial Complexes. Discrete Comput Geom 62, 164–179 (2019). https://doi.org/10.1007/s00454-019-00091-0

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  • DOI: https://doi.org/10.1007/s00454-019-00091-0

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