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

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

2003-11-09

arxiv.org/abs/math/0311127v1

Journal of Mathematical Sciences, vol 131, no 2, 2005, pp 5520-5537

Mathematics

Probability

27 pages, 5 figures, LaTeX

Scientific paper

10.1007/s10958-005-0424-4

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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