# 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…

## 10 Citations

Random walk on the random connection model

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Percolation phase transition in weight-dependent random connection models

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Abstract We investigate spatial random graphs defined on the points of a Poisson process in d-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson…

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Cover and Hitting Times of Hyperbolic Random Graphs

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. We study random walks on the giant component of Hyperbolic Random Graphs (HRGs), in the regime when the degree distribution obeys a power law with exponent in the range (2 , 3). In particular, we…

Chemical Distance in Geometric Random Graphs with Long Edges and Scale-Free Degree Distribution

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We study geometric random graphs defined on the points of a Poisson process in d-dimensional space, which additionally carry independent random marks. Edges are established at random using the marks…

Scale-free percolation mixing time

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Assign to each vertex of the one-dimensional torus i.i.d. weights with a heavy-tail of index τ − 1 > 0. Connect then each couple of vertices with probability roughly proportional to the product of…

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Transience Versus Recurrence for Scale-Free Spatial Networks

- Mathematics, Computer ScienceWAW
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Recurrence or transience of weight-dependent random connection graphs, features that are relevant for the performance of search and information diffusion algorithms on the network, are discussed.

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