11 papers
Absence of percolation in graphs based on stationary point processes with degrees bounded by two
Benedikt Jahnel, András Tóbiás
We consider undirected graphs that arise as deterministic functions of stationary point processes such that each point has degree bounded by two. For a large class of point process…
The interplay of dormancy and transfer in bacterial populations: Invasion, fixation and coexistence regimes
Jochen Blath, András Tóbiás
We investigate the interplay between two fundamental mechanisms of microbial population dynamics and evolution called dormancy and horizontal gene transfer. The corresponding trait…
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…
Particle systems with coordination
Adrián González Casanova, Noemi Kurt, András Tóbiás
We consider a generalization of spatial branching coalescing processes in which the behaviour of individuals is not (necessarily) independent, on the contrary, individuals tend to…
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…
A Gibbsian model for message routeing in highly dense multihop networks
Wolfgang König, András Tóbiás
We investigate a probabilistic model for routeing of messages in relay-augmented multihop ad-hoc networks, where each transmitter sends one message to the origin. Given the (random…
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…
The axiom system of classical harmony
András József Tóbiás
This paper provides a new mathematical axiom system for classical harmony, which is a prescriptive rule system for composing music, introduced in the second half of the 18th centur…