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

Maxim Krikun

Published 2003-11-09Version 1

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.