Research

Research profile

I study geometric random graphs and dependent percolation using multi-scale and geometric techniques. You can also browse my profiles on arXiv and ORCID.

Below you can see a pair of interactive browser simulations that illustrate some of the probabilistic structures that appear in my current research. Both run in real time and are designed to make the qualitative behaviour of the models tangible:

• Contact process on a mobile geometric graph - a live SIS epidemic spreading through nodes that move by Lévy flight and connect via Pareto-distributed radii.
• Lévy flight vs Brownian motion - a visual comparison of the two processes showing how heavy-tailed jumps produce qualitatively different path geometry.

Submitted papers and preprints

• Detection, coverage and percolation in dynamic Boolean models with random radii based on $\alpha$-stable processes Preprint
  with Benedikt Jahnel, Lukas Lüchtrath and Anh Duc Vu, arXiv:2602.22109
• Chemical distance in the Poisson Boolean model with regularly varying diameters Preprint
  with Marilyn Korfhage, arXiv:2503.18577
• Robustness in the Poisson Boolean model with convex grains Preprint
  with Marilyn Korfhage and Peter Mörters, arXiv:2410.13366
• Geometric scale-free random graphs on mobile vertices: broadcast and percolation times Preprint
  with Arne Grauer, arXiv:2404.15124

Published and accepted papers

• Lipschitz cutset for fractal graphs and applications to the spread of infections
  with Alexander Drewitz and Gioele Gallo, Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, to appear
• Finiteness of the percolation threshold for inhomogeneous long-range models in one dimension Published
  with Lukas Lüchtrath and Christian Mönch, Electronic Journal of Probability, 30: 1-29 (2025)
• The contact process on scale-free geometric random graphs Published
  with Arne Grauer, Stochastic Processes and their Applications, Volume 173: 104360 (2024)
• The Emergence of a Giant Component in One-Dimensional Inhomogeneous Networks with Long-Range Effects Published
  with Lukas Lüchtrath and Christian Mönch, Algorithms and Models for the Web Graph, WAW 2023: 19-35 (2023)
• Chemical distance in geometric random graphs with long edges and scale-free degree distribution Published
  with Arne Grauer and Peter Mörters, Communications in Mathematical Physics, 395: 859-906 (2022)
• Recurrence versus Transience for Weight-Dependent Random Connection Models Published
  with Markus Heydenreich, Christian Mönch and Peter Mörters, Electronic Journal of Probability, 27: 1-31 (2022)
• Percolation phase transition in weight-dependent random connection models Published
  with Lukas Lüchtrath and Peter Mörters, Advances in Applied Probability, 53(4), 1090-1114 (2021)
  Part of the June 2025 Applied Probability Collection on phase transitions.
• Transience Versus Recurrence for Scale-Free Spatial Networks Published
  with Markus Heydenreich, Christian Mönch and Peter Mörters, Algorithms and Models for the Web Graph, WAW 2020: 96-110 (2020)
• Random walks in random conductances: decoupling and spread of infection Published
  with Alexandre Stauffer, Stochastic Processes and their Applications, 129: 3547-3569 (2019)
• The age-dependent random connection model Published
  with Arne Grauer, Lukas Lüchtrath and Peter Mörters, Queueing Systems, 93: 309-331 (2019)
• Multi-scale Lipschitz percolation of increasing events for Poisson random walks Published
  with Alexandre Stauffer, Annals of Applied Probability, 29: 376-433 (2019)
• Percolation of Lipschitz surface and tight bounds on the spread of information among mobile agents Published
  with Alexandre Stauffer, APPROX-RANDOM 2018, 39: 1-17 (2018)

Collaborators

Alexander Drewitz , Gioele Gallo , Arne Grauer , Markus Heydenreich , Benedikt Jahnel , Marilyn Korfhage , Lukas Lüchtrath , Christian Mönch , Peter Mörters , Alexandre Stauffer , Anh Duc Vu

Selected conferences and workshops

• Long-range phenomena in Percolation, Cologne, Germany (2024)
• Stochastic Geometry in Action, Bath, UK (2024)
• Dynamic spatial random systems, Berlin, Germany (2024)
• Recent Trends in Spatial Stochastic Processes, Eindhoven, Netherlands (2022)
• Random Geometric Systems: First Annual Conference, Berlin, Germany (2022)
• Spatial Networks and Percolation, Oberwolfach, Germany (2021)
• YEP XV "Information Diffusion on Random Networks", Eindhoven, Netherlands (2019)
• APPROX/RANDOM 2018, Princeton, USA (2018)
• Strongly Correlated Random Interacting Processes, Oberwolfach, Germany (2018)