Growth of Uniform Infinite Causal Triangulations

Autor(es)

Sisko, V. ^[1] ; Yambartsev, A. ^[2] ; Zohren, S. ^{[2, 3, 4]}

Afiliação do(s) autor(es)

^[1] Univ Fed Fluminense, Dept Stat, BR-24020140 Niteroi, RJ - Brazil

^[2] Univ Sao Paulo, Dept Stat, BR-05508090 Sao Paulo - Brazil

^[3] PUC Rio de Janeiro, Dept Phys, BR-22451900 Rio De Janeiro - Brazil

^[4] Univ Oxford, Rudolf Peierls Ctr Theoret Phys, Oxford OX1 3NP - England

• Tipo de documento: Artigo Científico
• Fonte: Journal of Statistical Physics; v. 150, n. 2, p. 353-374, JAN 2013.
• Citações Web of Science: 4

Resumo

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. (AU)

• Processo FAPESP: 10/05891-2 - Aspectos probabilísticos de triangulações dinâmicas causais: percolação
• Beneficiário: Anatoli Iambartsev
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional