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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

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.

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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. https://doi.org/10.1214/17-BJPS356

Information

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

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Vol.32 • No. 3 • August 2018
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