3 papers
math.PR2025
Chemical distance in the Poisson Boolean model with regularly varying diameters
Peter Gracar, Marilyn Korfhage
We study the Poisson Boolean model with convex bodies which are rotation-invariant distributed. We assume that the convex bodies have regularly varying diameters with indices $-α_1…
math.PR2018
The age-dependent random connection model
Peter Gracar, Arne Grauer, Lukas Lüchtrath +1
We investigate a class of growing graphs embedded into the -dimensional torus where new vertices arrive according to a Poisson process in time, are randomly placed in space and…
cs.DM2018
Percolation of Lipschitz surface and tight bounds on the spread of information among mobile agents
Peter Gracar, Alexandre Stauffer
We consider the problem of spread of information among mobile agents on the torus. The agents are initially distributed as a Poisson point process on the torus, and move as indepen…