Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the transience of processes defined on Galton--Watson trees   We introduce a simple technique for proving the transience of certain
processes defined on the random tree $\mathcal{G}$ generated by a supercritical
branching process. We prove the transience for once-reinforced random walks on
$\mathcal{G}$, that is, a generalization of a result of Durrett, Kesten and
Limic [Probab. Theory Related Fields 122 (2002) 567--592]. Moreover, we give a
new proof for the transience of a family of biased random walks defined on
$\mathcal{G}$. Other proofs of this fact can be found in [Ann. Probab. 16
(1988) 1229--1241] and [Ann. Probab. 18 (1990) 931--958] as part of more
general results. A similar technique is applied to a vertex-reinforced jump
process. A by-product of our result is that this process is transient on the
3-ary tree. Davis and Volkov [Probab. Theory Related Fields 128 (2004) 42--62]
proved that a vertex-reinforced jump process defined on the $b$-ary tree is
transient if $b\ge 4$ and recurrent if $b=1$. The case $b=2$ is still open.

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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
27
The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph