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arXiv · 1502.07657

Stochastic Ordering of Infinite Geometric Galton-Watson Trees

Erik I. Broman
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Abstract

We consider Galton-Watson trees with Geom$(p)$ offspring distribution. We let $T_{\infty}(p)$ denote such a tree conditioned on being infinite. We prove that for any $1/2\leq p_1 <p_2 \leq 1$, there exists a coupling between $T_{\infty}(p_1)$ and $T_{\infty}(p_2)$ such that ${\mathbb P}(T_{\infty}(p_1) \subseteq T_{\infty}(p_2))=1.$

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Erik I. Broman. 2015-02-26. Stochastic Ordering of Infinite Geometric Galton-Watson Trees. https://arxiv.org/abs/1502.07657

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