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arXiv · 1201.0264

A note on weak convergence results for uniform infinite causal triangulations

V. Sisko·A. Yambartsev·S. Zohren
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Abstract

We discuss uniform 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 weak convergence of the joint length-area process of a uniform 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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V. Sisko, A. Yambartsev, S. Zohren. 2011-12-31. A note on weak convergence results for uniform infinite causal triangulations. https://arxiv.org/abs/1201.0264

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