Peter Gracar

activity

20172026

most citedRecurrence versus Transience for Weight-Dependent Random Connection Models

32 citations · 92 across the 16 of their papers we have counts for

collaborators

Showing 2026 · math.PRShow all

3 papers · 2 filters

math.PR2026

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 $R^{d}$ of intensity $η$ . Two particles are in contact when their distance is at m…

math.PR2026

Rainbow percolation

Peter Gracar, Benjamin Lees

We consider the weight-dependent random connection model on a Poisson point process of intensity $λ$ on $R \times (0, 1)$ in which the vertices $(x, t)$ and $(y, s)$ are joined…

math.PR2026

Detection, coverage and percolation in dynamic Boolean models with random radii based on $α$ -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 $α$ -stable pro…

Motion helps the contact process: survival below the percolation threshold on Poisson Brownian motions

Rainbow percolation

Detection, coverage and percolation in dynamic Boolean models with random radii based on α-stable processes

Detection, coverage and percolation in dynamic Boolean models with random radii based on $α$ -stable processes