Growth of uniform infinite causal triangulations
Mathematical Physics
2013-02-06 v2 math.MP
Probability
Abstract
We introduce a growth process which samples sections of uniform infinite causal triangulations by elementary moves in which a single triangle is added. A relation to a random walk on the integer half line is shown. This relation is used to estimate the geodesic distance of a given triangle to the rooted boundary in terms of the time of the growth process and to determine from this the fractal dimension. Furthermore, convergence of the boundary process to a diffusion process is shown leading to an interesting duality relation between the growth process and a corresponding branching process.
Keywords
Cite
@article{arxiv.1203.2869,
title = {Growth of uniform infinite causal triangulations},
author = {V. Sisko and A. Yambartsev and S. Zohren},
journal= {arXiv preprint arXiv:1203.2869},
year = {2013}
}
Comments
27 pages, 6 figures, small changes, as published