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

Maxim Krikun
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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.

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Maxim Krikun. 2003-11-09. Uniform infinite planar triangulation and related time-reversed critical branching process. https://doi.org/10.1007/s10958-005-0424-4

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