6 papers
Phase transitions for the Boolean model of continuum percolation for Cox point processes
Benedikt Jahnel, András Tóbiás, Elie Cali
We consider the Boolean model with random radii based on Cox point processes. Under a condition of stabilization for the random environment, we establish existence and non-existenc…
SINR percolation for Cox point processes with random powers
Benedikt Jahnel, András Tóbiás
Signal-to-interference plus noise ratio (SINR) percolation is an infinite-range dependent variant of continuum percolation modeling connections in a telecommunication network. Unli…
Lower large deviations for geometric functionals
Christian Hirsch, Benedikt Jahnel, András Tóbiás
This work develops a methodology for analyzing large-deviation lower tails associated with geometric functionals computed on a homogeneous Poisson point process. The technique appl…
Invasion and fixation of microbial dormancy traits under competitive pressure
Jochen Blath, András Tóbiás
Microbial dormancy is an evolutionary trait that has emerged independently at various positions across the tree of life. It describes the ability of a microorganism to switch to a…
Signal to interference ratio percolation for Cox point processes
András Tóbiás
We study the signal-to-interference ratio (SINR) percolation model for a stationary Cox point process in two or higher dimensions, in case of a bounded and integrable path-loss fun…
Highly dense mobile networks with random fadings
András József Tóbiás
Master thesis at TU Berlin with Wolfgang König, April 2016. We investigate a wireless network where the users are located according to a Poisson point process in a bounded subset o…