Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic Ordering of Infinite Binomial Galton-Watson Trees   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 ${\mathbb
P}(T_{\infty}(p_1) \subseteq T_{\infty}(p_2))=1.$

27
The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph