Project
EF45-3
Data Transmission in Dynamical Random Networks
Project Heads
Benedikt Jahnel
Project Members
Anh Duc Vu (08/24 – 03/26), Julia Hörrmann (03/24 – 07/24)
Project Duration
01.03.2024 – 31.03.2026
Located at
WIAS
Description
An overwhelming need for data transmission in a globalised world calls for massive innovations in the design of future networks. The project aims to contribute to this via the rigorous analysis of detection and contact times in complex networks featuring realistic mobility and multifaceted sources of randomness.
Project Webpages
Selected Publications
- P. Gracar, B. Jahnel, L. Lüchtrath, A.D. Vu: Detection, coverage and percolation in dynamic Boolean models with random radii based on alpha-stable processes, Preprint available at arXiv:2602.22109
- B. Jahnel, P. Ghosh: Coexistence for competing branching random walks with identical asymptotic shape on Z^d,
Preprint available at arXiv:2512.09153 - J. Bäumler, B. Jahnel, J. Köppl, B. Lodewijks, L. Reeves, A. Tóbiás: Local criteria for global connectivity comparisons: beyond stochastic domination, Preprint available at arXiv:2510.03934
- C. Hirsch, B. Jahnel, P. Juhasz: Functional limit theorems for edge counts in dynamic random connection hypergraphs,
Preprint available at arXiv:2507.16270 - B. Jahnel, L. Lüchtrath, A.D. Vu: Oriented bond-site percolation in random environment and contact processes with periodic recovery, Preprint available at arXiv:2507.00329
- P. Ghosh, B. Jahnel, Y. Steenbeck: Throughput in inhomogeneous planar drainage networks,
Preprint available at arXiv:2506.18132 - B. Jahnel, L. Lüchtrath, D. Mönch: Phase transitions for contact processes on sparse random graphs via metastability and local limits, Preprint available at arXiv:2505.22471
- B. Jahnel, L. Lüchtrath, D. Mönch: Phase transitions for contact processes on one-dimensional networks,
Preprint available at arXiv:2501.16858 - B. Jahnel, L. Lüchtrath, E. Jacob: Subcritical annulus crossing in spatial random graphs,
Preprint available at arXiv:2411.10333 - B. Jahnel, L. Lüchtrath, M. Ortgiese: Cluster sizes in subcritical soft Boolean models,
Preprint available at arXiv:2404.13730 - D. Coupier, B. Henry, B. Jahnel, J. Köppl: The planar lattice two-neighbor graph percolates,
Accepted at Annals of Probability, also available at arXiv:2412.20781 - B. Jahnel, L. Lüchtrath, A.D. Vu: First contact percolation,
Bernoulli 2026, Vol. 32, No. 2, 1594-1619 (2026) - B. Jahnel, S. Jhawar, P. Ghosh: Large and moderate deviations in Poisson navigations,
Journal of Applied Probability (2025) - B. Jahnel, J. Köppl, B. Lodewijks, A. Tóbiás: Percolation in lattice k-neighbor graphs,
Journal of Applied Probability Vol. 62, No. 4, 1475–1492 (2025 - C. Hirsch, B. Jahnel, S. Jhawar, P. Juhasz: Poisson approximation of fixed-degree nodes in weighted random connection models, Stochastic Processes and their Applications Vol. 183 (2025)
- M. Heida, B. Jahnel, A.D. Vu: Stochastic homogenization on irregularly perforated domains,
Networks and Heterogeneous Media Vol. 20, No. 1, 165-212 (2025) - M. Heida, B. Jahnel, A.D. Vu: An ergodic and isotropic zero-conductance model with arbitrarily strong local connectivity,
Electronic Communications in Probability Vol. 29, No. 66, 1-13 (2024)
Selected Pictures
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Connectivity in central and decentral communication
Illustration of decentral and central communication. The mobile phones are a Poisson point process in the square [0,400]^2 with intensity 0.000125 per m^2.
Illustration of a contact based percolation model
Simulation of the set of devices reachable from the origin in a device-to-device network after 10 and 50 days. The set is scaled by the inverse time. We assume that each device has one contact per day at a random time with each of its neighbours.
Detection in dynamic Boolean models based on alpha-stable processes
Illustration of moving point cloud based on iid jump processes with individual marks representing balls of interaction.