44 citations · 181 across the 27 of their papers we have counts for
33 papers
Markov Renewal Theory for Transfer Operators and Point Processes on the Line
Yoon Jun Chan, Markus Heydenreich, Sabine Jansen
We prove exponential decay of pair correlations for 1D stationary point processes when spacings satisfy a Markov condition, geometric ergodicity, and a condition on exponential mom…
Bi-infinite incipient cluster in high dimensions
Manuel Cabezas, Alexander Fribergh, Markus Heydenreich +1
We consider high-dimensional percolation at the critical threshold. We condition the origin to be disjointly connected to two points, and , and subsequently take the limit…
Expansion of the Critical Intensity for the Random Connection Model
Matthew Dickson, Markus Heydenreich
We derive an asymptotic expansion for the critical percolation density of the random connection model as the dimension of the encapsulating space tends to infinity. We calculate ri…
The Triangle Condition for the Marked Random Connection Model
Matthew Dickson, Markus Heydenreich
We investigate a spatial random graph model whose vertices are given as a marked Poisson process on . Edges are inserted between any pair of points independently with…
Prudent walk in dimension six and higher
Markus Heydenreich, Lorenzo Taggi, Niccolo Torri
We study the high-dimensional uniform prudent self-avoiding walk, which assigns equal probability to all nearest-neighbor self-avoiding paths of a fixed length that respect the pru…
Graph distances in scale-free percolation: the logarithmic case
Nannan Hao, Markus Heydenreich
Scale-free percolation is a stochastic model for complex networks. In this spatial random graph model, vertices are linked by an edge with probability dependin…