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Uniform Infinite Planar Triangulations

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Abstract

The existence of the weak limit as n→∞ of the uniform measure on rooted triangulations of the sphere with n vertices is proved. Some properties of the limit are studied. In particular, the limit is a probability measure on random triangulations of the plane.

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Authors and Affiliations

  1. Department of Mathematics, Weizmann Institute of science, Rehovot, 76100, Israel

    Omer Angel

  2. Microsoft Corporation, One Microsoft Way, Redmond, WA, 98052, USA

    Oded Schramm

Authors
  1. Omer Angel
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  2. Oded Schramm
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Correspondence to Omer Angel.

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Communicated by M. Aizenman

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Angel, O., Schramm, O. Uniform Infinite Planar Triangulations. Commun. Math. Phys. 241, 191–213 (2003). https://doi.org/10.1007/s00220-003-0932-3

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  • DOI: https://doi.org/10.1007/s00220-003-0932-3

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