Growth of Uniform Infinite Causal Triangulations

V. Sisko, A. Yambartsev, S. Zohren
<span title="">2013</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="" style="color: black;">Journal of statistical physics</a> </i> &nbsp;
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
more &raquo; ... n interesting duality relation between the growth process and a corresponding branching process.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1007/s10955-012-0665-9</a> <a target="_blank" rel="external noopener" href="">fatcat:r3eoy7sesrah3f3bhrqdu3nqbi</a> </span>
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