Uniform infinite planar triangulation and related time-reversed critical branching process

Abstract

We establish a connection between the uniform infinite planar triangulation and some critical time-reversed branching process. This allows to find a scaling limit for the principal boundary component of a ball of radius R for large R (i.e. for a boundary component separating the ball from infinity). We show also that outside of R-ball a contour exists that has length linear in R.

27 pages, 5 figures, LaTeX

References in corpus (2)

• Uniform Infinite Planar Triangulations
• Scaling in quantum gravity

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