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Uniform Infinite Planar Triangulations

arXiv:math/0207153 · doi:10.1007/s00220-003-0932-3

Abstract

The existence of the weak limit as n --> infinity 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.

36 pages, 4 figures; Journal revised version