Coupling on weighted branching trees

Ningyuan Chen; Mariana Olvera-Cravioto

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arXiv · 1410.1050

Coupling on weighted branching trees

Ningyuan Chen·Mariana Olvera-Cravioto

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Abstract

This paper considers linear functions constructed on two different weighted branching processes and provides explicit bounds for their Kantorovich-Rubinstein distance in terms of couplings of their corresponding generic branching vectors. Motivated by applications to the analysis of random graphs, we also consider a variation of the weighted branching process where the generic branching vector has a different dependence structure from the usual one. By applying the bounds to sequences of weighted branching processes, we derive sufficient conditions for the convergence in the Kantorovich-Rubinstein distance of linear functions. We focus on the case where the limits are endogenous fixed points of suitable smoothing transformations.

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Ningyuan Chen, Mariana Olvera-Cravioto. 2015-06-25. Coupling on weighted branching trees. https://arxiv.org/abs/1410.1050

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