Growth of uniform infinite causal triangulations

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.

27 pages, 6 figures, small changes, as published

References in corpus (4)

• The spectral dimension of generic trees
• A Matrix Model for 2D Quantum Gravity defined by Causal Dynamical Triangulations
• A new continuum limit of matrix models
• Growth of uniform infinite causal triangulations

Cited by in corpus (1)

• Growth of uniform infinite causal triangulations