Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Contact Process on Periodic Trees   A little over 25 years ago Pemantle pioneered the study of the contact
process on trees, and showed that on homogeneous trees the critical values
$\lambda_1$ and $\lambda_2$ for global and local survival were different. He
also considered trees with periodic degree sequences, and Galton-Watson trees.
Here, we will consider periodic trees in which the number of children in
successive generation is $(n,a_1,\ldots, a_k)$ with $\max_i a_i \le
Cn^{1-\delta}$ and $\log(a_1 \cdots a_k)/\log n \to b$ as $n\to\infty$. We show
that the critical value for local survival is asymptotically $\sqrt{c (\log
n)/n}$ where $c=(k-b)/2$. This supports Pemantle's claim that the critical
value is largely determined by the maximum degree, but it also shows that the
smaller degrees can make a significant contribution to the answer.

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The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
1
The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas