Random Planar Geometry

  • Itai Benjamini
Part of the Lecture Notes in Mathematics book series (LNM, volume 2100)


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.


Planar Graph Simple Random Walk Injectivity Radius Pant Decomposition Vertex Transitive Graph 
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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Itai Benjamini
    • 1
  1. 1.Department of MathematicsThe Weizmann Institute of ScienceRehovotIsrael

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