Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Galton-Watson trees with first ancestor interaction   We consider the set of random Bienaym\'e-Galton-Watson trees with a bounded
number of offspring and bounded number of generations as a statistical
mechanics model: a random tree is a rooted subtree of the maximal tree; the
spin at a given node of the maximal tree is equal to the number of offspring if
the node is present in the random tree and equal to -1 otherwise. We introduce
nearest neighbour interactions favouring pairs of neighbours which both have a
relatively large offspring. We then prove (1) correlation inequalities and (2)
recursion relations for generating functions, mean number of leaves,
interaction energy and the corresponding variances. The resulting quadratic
dynamical system, in two dimensions or more depending on the desired number of
moments, yields almost exact numerical results. The balance between offspring
distribution and coupling constant leads to a phase diagram for the analogue of
the extinction probability. On the transition line the mean number of leaves in
generation $n$ is found numerically to scale as $n^{-2}$.

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph