Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recurrence or transience of random walks on random graphs generated by
  point processes in $\mathbb{R}^d$   We consider random walks associated with conductances on Delaunay
triangulations, Gabriel graphs and skeletons of Voronoi tilings which are
generated by point processes in $\mathbb{R}^d$. Under suitable assumptions on
point processes and conductances, we show that, for almost any realization of
the point process, these random walks are recurrent if $d=2$ and transient if
$d\geq 3$. These results hold for a large variety of point processes including
Poisson point processes, Mat{\'e}rn cluster and Mat{\'e}rn hardcore processes
which have clustering or repulsive properties. In order to prove them, we state
general criteria for recurrence or almost sure transience which apply to random
graphs embedded in $\mathbb{R}^d$.

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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org