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Random Planar Geometry

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Coarse Geometry and Randomness

Part of the book series: Lecture Notes in Mathematics ((LNMECOLE,volume 2100))

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Abstract

What is a typical random surface? This question has arisen in the theory of two-dimensional quantum gravity where discrete triangulations have been considered as a discretization of a random continuum Riemann surface. As we will see the typical random surface has a geometry which is very different from the one of the Euclidean plane.

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Notes

  1. 1.

    The real theorem actually deals directly with maps.

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Authors and Affiliations

  1. Department of Mathematics, The Weizmann Institute of Science, Rehovot, Israel

    Itai Benjamini

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  1. Itai Benjamini
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Benjamini, I. (2013). Random Planar Geometry. In: Coarse Geometry and Randomness. Lecture Notes in Mathematics(), vol 2100. Springer, Cham. https://doi.org/10.1007/978-3-319-02576-6_6

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