%0 Journal Article
%T Stochastic Ordering of Infinite Binomial Galton-Watson Trees
%A Erik I. Broman
%J Mathematics
%D 2014
%I arXiv
%X We consider Galton-Watson trees with ${\rm Bin}(d,p)$ offspring distribution. We let $T_{\infty}(p)$ denote such a tree conditioned on being infinite. For $d=2,3$ and any $1/d\leq p_1 <p_2 \leq 1$, we show that there exists a coupling between $T_{\infty}(p_1)$ and $T_{\infty}(p_2)$ such that ${\mathbb P}(T_{\infty}(p_1) \subseteq T_{\infty}(p_2))=1.$
%U http://arxiv.org/abs/1403.4834v1