4 papers
Flexibility versus genericity of phase diagrams of perturbed continuous maps on the Cantor set
Hugo Marsan, Mathieu Sablik
Consider the dynamical system constitued by a continuous function where is a finite alphabet. The perturbed counte…
A perturbed cellular automaton with two phase transitions for the ergodicity
Hugo Marsan, Mathieu Sablik, Ilkka Törmä
The positive rates conjecture states that a one-dimensional probabilistic cellular automaton (PCA) with strictly positive transition rates must be ergodic. The conjecture has been…
Characterization of the set of zero-noise limits measures of perturbed cellular automata
Hugo Marsan, Mathieu Sablik
We add small random perturbations to a cellular automaton and consider the one-parameter family parameterized by where is the level of noise. The objective…
Strong stochastic stability of cellular automata
Hugo Marsan, Mathieu Sablik
We define the notion of stochastic stability, already present in the literature in the context of smooth dynamical systems, for invariant measures of cellular automata perturbed by…