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math.PR2026
Gilbert's disc model conditioned on the square lattice
Jérôme Casse, Irène Marcovici, Maxence Poutrel
The paper defines a percolation model on the 2‑D integer lattice by placing a uniformly random point in each unit cell and connecting points whose Euclidean distance is below a rad…
math.PR2025
Ergodicity of the hard-core PCA with a random walk method
Jérôme Casse, Irène Marcovici, Maxence Poutrel
The hard-core probabilistic cellular automaton has attracted a renewed interest in the last few years, thanks to its connection with the study of a combinatorial game on percolatio…