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Journal articles
Planar maps, circle patterns and 2d gravity
Abstract : Via circle pattern techniques, random planar triangulations (with angle variables) are mapped onto Delaunay triangulations in the complex plane. The uniform measure on triangulations is mapped onto a conformally invariant spatial point process. We show that this measure can be expressed as: (1) a sum over 3-spanning-trees partitions of the edges of the Delaunay triangulations; (2) the volume form of a Kähler metric over the space of Delaunay triangulations, whose prepotential has a simple formulation in term of ideal tessellations of the 3d hyperbolic space $\mathbb{H}_3$; (3) a discretized version (involving finite difference complex derivative operators $\nabla,\bar\nabla$) of Polyakov's conformal Fadeev-Popov determinant in 2d gravity; (4) a combination of Chern classes, thus also establishing a link with topological 2d gravity.
Cited literature [31 references]
https://hal-cea.archives-ouvertes.fr/cea-01509872
Contributor : Emmanuelle de Laborderie <>
Submitted on : Tuesday, April 18, 2017 - 4:15:35 PM
Last modification on : Thursday, November 26, 2020 - 10:00:03 AM
Long-term archiving on: : Wednesday, July 19, 2017 - 3:18:39 PM
Contributor : Emmanuelle de Laborderie <>
Submitted on : Tuesday, April 18, 2017 - 4:15:35 PM
Last modification on : Thursday, November 26, 2020 - 10:00:03 AM
Long-term archiving on: : Wednesday, July 19, 2017 - 3:18:39 PM
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1307.3123.pdf
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