Growth and Percolation on the Uniform Infinite Planar Triangulation
| dc.creator | Angel, Omer | |
| dc.date | 2002-08-15 | |
| dc.date.accessioned | 2026-07-07T04:50:16Z | |
| dc.date.available | 2026-07-07T04:50:16Z | |
| dc.description | A construction as a growth process for sampling of the uniform infinite planar triangulation (UIPT), defined in a previous paper, is given. The construction is algorithmic in nature, and is an efficient method of sampling a portion of the UIPT. By analyzing the progress rate of the growth process we show that a.s. the UIPT has growth rate r^4 up to polylogarithmic factors, confirming heuristic results from the physics literature. Additionally, the boundary component of the ball of radius r separating it from infinity a.s. has growth rate r^2 up to polylogarithmic factors. It is also shown that the properly scaled size of a variant of the free triangulation of an m-gon converges in distribution to an asymmetric stable random variable of type 1/2. By combining Bernoulli site percolation with the growth process for the UIPT, it is shown that a.s. the critical probability p_c=1/2 and that at p_c percolation does not occur. | |
| dc.identifier | https://arxiv.org/abs/math/0208123 | |
| dc.identifier | http://arxiv.org/abs/math/0208123 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64729 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 05C80; 05C30, 82B43, 81T40 | |
| dc.title | Growth and Percolation on the Uniform Infinite Planar Triangulation | |
| dc.type | text |