32 citations · 92 across the 16 of their papers we have counts for
16 papers
Motion helps the contact process: survival below the percolation threshold on Poisson Brownian motions
Peter Gracar
We consider the SIS contact process on a Poisson system of independent Brownian motions in of intensity . Two particles are in contact when their distance is at m…
Rainbow percolation
Peter Gracar, Benjamin Lees
We consider the weight-dependent random connection model on a Poisson point process of intensity on in which the vertices and are joined…
Detection, coverage and percolation in dynamic Boolean models with random radii based on -stable processes
Peter Gracar, Benedikt Jahnel, Lukas Lüchtrath +1
We consider a dynamic network in continuum time and space in which nodes, with initial locations given by a Poisson point process, move according to i.i.d. isotropic -stable pro…
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…
Robustness in the Poisson Boolean model with convex grains
Peter Gracar, Marilyn Korfhage, Peter Mörters
We study the Poisson Boolean model where the grains are random convex bodies with a rotation-invariant distribution. A grain distribution is dense if the union of the grains covers…
Geometric scale-free random graphs on mobile vertices: broadcast and percolation times
Peter Gracar, Arne Grauer
We study the phenomenon of information propagation on mobile geometric scale-free random graphs, where vertices instantaneously pass on information to all other vertices in the sam…
Lipschitz cutset for fractal graphs and applications to the spread of infections
Alexander Drewitz, Gioele Gallo, Peter Gracar
We consider the fractal Sierpiński gasket or carpet graph in dimension denoted by . At time , we place a Poisson point process of particles onto the graph and let…
The contact process on scale-free geometric random graphs
Peter Gracar, Arne Grauer
We study the contact process on a class of geometric random graphs with scale-free degree distribution, defined on a Poisson point process on . This class includes th…
Finiteness of the percolation threshold for inhomogeneous long-range models in one dimension
Peter Gracar, Lukas Lüchtrath, Christian Mönch
We consider inhomogeneous spatial random graphs on the real line. Each vertex carries an i.i.d. weight and edges are drawn such that short edges and edges to vertices with large we…
Chemical distance in geometric random graphs with long edges and scale-free degree distribution
Peter Gracar, Arne Grauer, Peter Mörters
We study geometric random graphs defined on the points of a Poisson process in -dimensional space, which additionally carry independent random marks. Edges are established at ra…
Percolation phase transition in weight-dependent random connection models
Peter Gracar, Lukas Lüchtrath, Peter Mörters
We investigate spatial random graphs defined on the points of a Poisson process in -dimensional space, which combine scale-free degree distributions and long-range effects. Ever…
Recurrence versus Transience for Weight-Dependent Random Connection Models
Peter Gracar, Markus Heydenreich, Christian Mönch +1
We investigate random graphs on the points of a Poisson process in -dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point…
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…
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…
Multi-scale Lipschitz percolation of increasing events for Poisson random walks
Peter Gracar, Alexandre Stauffer
Consider the graph induced by , equipped with uniformly elliptic random conductances. At time , place a Poisson point process of particles on and le…
Random walks in random conductances: decoupling and spread of infection
Peter Gracar, Alexandre Stauffer
Let be a uniformly elliptic random conductance graph on with a Poisson point process of particles at time that perform independent simple random walks.…