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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

A note on weak convergence results for infinite causal triangulations

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Author(s):
Sisko, Valentin [1] ; Yambartsev, Anatoly [2] ; Zohren, Stefan [3]
Total Authors: 3
Affiliation:
[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
Total Affiliations: 3
Document type: Journal article
Source: BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS; v. 32, n. 3, p. 597-615, AUG 2018.
Web of Science Citations: 0
Abstract

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)

FAPESP's process: 10/05891-2 - Probabilistic aspects of causal dynamical triangulations: percolation
Grantee:Anatoli Iambartsev
Support Opportunities: Research Grants - Visiting Researcher Grant - International