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

Autor: Peter Morters, Arne Grauer, Peter Gracar

Publikováno v: Communications in Mathematical Physics. 395:859-906

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 of the endpoints and the distance between points

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https://doi.org/10.1007/s00220-022-04445-3

Percolation phase transition in weight-dependent random connection models

Autor: Peter Gracar, Peter Mörters, Lukas Lüchtrath

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 point is assigned an independent weight. Given the weight and

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Recurrence versus Transience for Weight-Dependent Random Connection Models

Autor: Peter Gracar, Markus Heydenreich, Christian Mönch, Peter Mörters

We investigate 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 mark and given marks and positions of th

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Multi-scale Lipschitz percolation of increasing events for Poisson random walks

Autor: Alexandre Stauffer, Peter Gracar

Publikováno v: Ann. Appl. Probab. 29, no. 1 (2019), 376-433
Gracar, P & Stauffer, A 2019, ' Multi-scale Lipschitz percolation of increasing events for Poisson random walks ', Annals of Applied Probability, vol. 29, no. 1, pp. 376-433 . https://doi.org/10.1214/18-AAP1420

Consider the graph induced by $\mathbb{Z}^d$, equipped with uniformly elliptic random conductances. At time $0$, place a Poisson point process of particles on $\mathbb{Z}^d$ and let them perform independent simple random walks. Tessellate the graph i

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https://www.scopus.com/inward/record.uri?eid=2-s2.0-85058466856&doi=10.1214/18-AAP1420&partnerID=40&md5=23cd5d02931c6e36ab07fa6ae7d0a422