A note on weak convergence results for infinite causal triangulations

Autor(es)

Sisko, Valentin ^[1] ; Yambartsev, Anatoly ^[2] ; Zohren, Stefan ^[3]

Afiliação do(s) autor(es)

^[1] Univ Fed Fluminense, Dept Math, Rua Mario Santos Braga S-N, BR-24020140 Niteroi, RJ - Brazil

^[2] Univ Sao Paulo, Inst Math & Stat, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil

^[3] Univ Oxford, Dept Mat, Parks Rd, Oxford OX1 3PH - England

• Tipo de documento: Artigo Científico
• Fonte: BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS; v. 32, n. 3, p. 597-615, AUG 2018.
• Citações Web of Science: 0

Resumo

We discuss infinite causal triangulations and equivalence to the size biased branching process measure-the critical Galton-Watson branching process distribution conditioned on non-extinction. Using known results from the theory of branching processes, this relation is used to prove a novel weak convergence result of the joint length-area process of a infinite causal triangulations to a limiting diffusion. The diffusion equation enables us to determine the physical Hamiltonian and Green's function from the Feynman-Kac procedure, providing us with a mathematical rigorous proof of certain scaling limits of causal dynamical triangulations. (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