4 papers
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,…
Quasicrystalline Gibbs states in 4-dimensional lattice-gas models with finite-range interactions
Siamak Taati, Jacek Miȩkisz, Jacek MiÈ©kisz
We construct a four-dimensional lattice-gas model with finite-range interactions that has non-periodic, "quasicrystalline" Gibbs states at low temperatures. Such Gibbs states are p…
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…
Cellular automata, percolation and dynamical dichotomies
Sebastián Barbieri, Felipe GarcÃa-Ramos, Siamak Taati
We establish a connection between percolation on the Cayley graphs of a group and the dynamical diversity of cellular automata on that group. Specifically, we demonstrate that Gilm…