Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Localization Transition of Biased Random Walks on Random Networks   We study random walks on large random graphs that are biased towards a
randomly chosen but fixed target node. We show that a critical bias strength
b_c exists such that most walks find the target within a finite time when
b>b_c. For b<b_c, a finite fraction of walks drifts off to infinity before
hitting the target. The phase transition at b=b_c is second order, but finite
size behavior is complex and does not obey the usual finite size scaling
ansatz. By extending rigorous results for biased walks on Galton-Watson trees,
we give the exact analytical value for b_c and verify it by large scale
simulations.

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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: math
30
The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: stat