Thursday, March 15, 2012

1203.2869 (V. Sisko et al.)

Growth of uniform infinite causal triangulations    [PDF]

V. Sisko, A. Yambartsev, S. Zohren
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.
View original:

No comments:

Post a Comment