Research

I work on geometric random graphs and dependent percolation , mostly by multi-scale arguments. Recurring questions are how far apart two vertices of a scale-free spatial network are, whether a random walk or a contact process on it survives or spreads, when a Boolean model with moving or heavy-tailed grains covers or detects a target, and how Lipschitz surfaces control dependent percolation. Papers marked Simulation have an interactive simulation that runs in the browser.

My papers are also listed on arXiv and ORCID.

Preprints

• Motion helps the contact process: survival below the percolation threshold on Poisson Brownian motions⁠Preprint
  arXiv:2608.24830
• Rainbow percolation⁠PreprintSimulation
  with Benjamin Lees, arXiv:2608.12954
  Interactive simulation: an illustrated tour of the model
• Detection, coverage and percolation in dynamic Boolean models with random radii based on $\alpha$-stable processes⁠PreprintSimulations
  with Benedikt Jahnel, Lukas Lüchtrath and Anh Duc Vu, arXiv:2602.22109
  Interactive simulations: Lévy flight vs Brownian motion · detection and coverage times
• Chemical distance in the Poisson Boolean model with regularly varying diameters⁠Preprint
  with Marilyn Korfhage, arXiv:2503.18577
• Robustness in the Poisson Boolean model with convex grains⁠Preprint
  with Marilyn Korfhage and Peter Mörters, arXiv:2410.13366
• Geometric scale-free random graphs on mobile vertices: broadcast and percolation times⁠PreprintSimulation
  with Arne Grauer, arXiv:2404.15124
  Interactive simulation: an SIS epidemic on a mobile geometric graph

Published and accepted

• Lipschitz cutset for fractal graphs and applications to the spread of infections⁠Published
  with Alexander Drewitz and Gioele Gallo, Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, 62(2): 830-878 (2026)
• Finiteness of the percolation threshold for inhomogeneous long-range models in one dimension⁠Published
  with Lukas Lüchtrath and Christian Mönch, Electronic Journal of Probability, 30: 1-29 (2025)
• The contact process on scale-free geometric random graphs⁠PublishedSimulation
  with Arne Grauer, Stochastic Processes and their Applications, Volume 173: 104360 (2024)
  Interactive simulation: an SIS epidemic on a mobile geometric graph
• The Emergence of a Giant Component in One-Dimensional Inhomogeneous Networks with Long-Range Effects⁠Published
  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 distribution⁠Published
  with Arne Grauer and Peter Mörters, Communications in Mathematical Physics, 395: 859-906 (2022)
• Recurrence versus Transience for Weight-Dependent Random Connection Models⁠Published
  with Markus Heydenreich, Christian Mönch and Peter Mörters, Electronic Journal of Probability, 27: 1-31 (2022)
• Percolation phase transition in weight-dependent random connection models⁠Published
  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 Networks⁠Published
  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 infection⁠Published
  with Alexandre Stauffer, Stochastic Processes and their Applications, 129: 3547-3569 (2019)
• The age-dependent random connection model⁠Published
  with Arne Grauer, Lukas Lüchtrath and Peter Mörters, Queueing Systems, 93: 309-331 (2019)
• Multi-scale Lipschitz percolation of increasing events for Poisson random walks⁠Published
  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 agents⁠Published
  with Alexandre Stauffer, APPROX-RANDOM 2018, 39: 1-17 (2018)

Coauthors

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

Conferences and workshops

• Heavy-tailed phenomena in random discrete geometries, Cologne, Germany (2027)⁠
• Spreading dynamics in random environments, Berlin, Germany (2026)⁠
• LASR 2026: Statistics, Deep Learning and Graphical Models, Leeds, UK (2026)⁠
• 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)⁠