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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,…
math.PR2025
Zero-one laws for events with positional symmetries
Yahya Ayach, Anthony Khairallah, Tia Manoukian +3
We use an information-theoretic argument due to O'Connell (2000) to prove that every sufficiently symmetric event concerning a countably infinite family of independent and identica…