Recurrence versus transience for weight-dependent random connection models

@article{Gracar2022RecurrenceVT,
  title={Recurrence versus transience for weight-dependent random connection models},
  author={Peter Gracar and Markus Heydenreich and Christian Monch and Peter Morters},
  journal={Electronic Journal of Probability},
  year={2022}
}
We investigate a large class of random graphs on the points of a Poisson process in $d$-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point carries an independent random weight and given weight and position of the points we form an edge between two points independently with a probability depending on the two weights and the distance of the points. In dimensions $d\in\{1,2\}$ we completely characterise recurrence vs transience of random… 

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