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="https://fatcat.wiki/container/4izt5rrukjdxbkwmndfvobfuj4" 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="https://doi.org/10.1007/s10955-012-0665-9">doi:10.1007/s10955-012-0665-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/r3eoy7sesrah3f3bhrqdu3nqbi">fatcat:r3eoy7sesrah3f3bhrqdu3nqbi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200917170737/https://arxiv.org/pdf/1203.2869v1.pdf" title="fulltext PDF download [not primary version]" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/48/0c/480c478244f1079cabe5a854fa1ab7b8ac675931.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10955-012-0665-9"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>