Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First Order Probabilities For Galton-Watson Trees   In the regime of Galton-Watson trees, first order logic statements are
roughly equivalent to examining the presence of specific finite subtrees. We
consider the space of all trees with Poisson offspring distribution and show
that such finite subtrees will be almost surely present when the tree is
infinite. Introducing the notion of universal trees, we show that all first
order sentences of quantifier depth $k$ depend only on local neighbourhoods of
the root of sufficiently large radius depending on $k$. We compute the
probabilities of these neighbourhoods conditioned on the tree being infinite.
We give an almost sure theory for infinite trees.

16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex