Translator Disclaimer
August 2018 A note on weak convergence results for infinite causal triangulations
Valentin Sisko, Anatoly Yambartsev, Stefan Zohren
Braz. J. Probab. Stat. 32(3): 597-615 (August 2018). DOI: 10.1214/17-BJPS356


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.


Download Citation

Valentin Sisko. Anatoly Yambartsev. Stefan Zohren. "A note on weak convergence results for infinite causal triangulations." Braz. J. Probab. Stat. 32 (3) 597 - 615, August 2018.


Received: 1 November 2015; Accepted: 1 February 2017; Published: August 2018
First available in Project Euclid: 8 June 2018

zbMATH: 06930041
MathSciNet: MR3812384
Digital Object Identifier: 10.1214/17-BJPS356

Rights: Copyright © 2018 Brazilian Statistical Association


Vol.32 • No. 3 • August 2018
Back to Top