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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…