3 papers
math.PR2026
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…
math.PR2025
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…
math.PR2025
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…