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math.PR2026
Gilbert's disc model conditioned on the square lattice
Jérôme Casse, Irène Marcovici, Maxence Poutrel
We present a new percolation model on the two-dimensional lattice, which can be seen as a conditioned version of continuous percolation on the plane. Let us place a point uniformly…
math.PR2026
Positive-rate PCA and IPS with stationary Bernoulli measures are rapidly forgetful
Irène Marcovici, Siamak Taati
We prove that every probabilistic cellular automaton with strictly positive transition probabilities that admits a stationary Bernoulli measure is exponentially ergodic. Moreover,…