关于一致无限因果三角剖分弱收敛结果的注记
A note on weak convergence results for uniform infinite causal triangulations
摘要：
我们讨论了一致无限因果三角剖分和等价的大小偏置分支过程措施-临界Galton-Watson分支过程分布条件下的非灭绝。利用分支过程理论的已知结果，证明了均匀无限因果三角剖分的联合长度-面积过程弱收敛于极限扩散.扩散方程使我们能够确定的物理哈密顿量和格林函数的Feynman-Kac程序，为我们提供了一个严格的数学证明因果动力学三角形的某些标度限制。
英文摘要：
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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