Publication : t08/182

Confluence of geodesic paths and separating loops in large planar quadrangulations

Bouttier J. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
Guitter E. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
We consider planar quadrangulations with three marked vertices and discuss the geometry of triangles made of three geodesic paths joining them. We also study the geometry of minimal separating loops, i.e. paths of minimal length among all closed paths passing by one of the three vertices and separating the two others in the quadrangulation. We concentrate on the universal scaling limit of large quadrangulations, also known as the Brownian map, where pairs of geodesic paths or minimal separating loops have common parts of non-zero macroscopic length. This is the phenomenon of confluence, which distinguishes the geometry of random quadrangulations from that of smooth surfaces. We characterize the universal probability distribution for the lengths of these common parts.
Année de publication : 2009
Revue : J. Stat. Mech. P03001 (2009)
DOI : 10.1088/1742-5468/2009/03/P03001
Preprint : arXiv:0811.0509
Langue : Anglais

Fichier(s) à télécharger :
  • 1742-5468_2009_03_P03001.pdf
  • publi.pdf


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