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- W2950333707 abstract "The uniform infinite planar quadrangulation is an infinite random graph embedded in the plane, which is the local limit of uniformly distributed finite quadrangulations with a fixed number of faces. We study asymptotic properties of this random graph. In particular, we investigate scaling limits of the profile of distances from the distinguished point called the root, and we get asymptotics for the volume of large balls. As a key technical tool, we first describe the scaling limit of the contour functions of the uniform infinite well-labeled tree, in terms of a pair of eternal conditioned Brownian snakes. Scaling limits for the uniform infinite quadrangulation can then be derived thanks to an extended version of Schaeffer's bijection between well-labeled trees and rooted quadrangulations." @default.
- W2950333707 created "2019-06-27" @default.
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- W2950333707 date "2010-05-11" @default.
- W2950333707 modified "2023-09-27" @default.
- W2950333707 title "Scaling limits for the uniform infinite quadrangulation" @default.
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