MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Has the following conjecture been prooved, or has any step in the direction of its proof been done?

"ANY Probabilistic Cellular Automata converge fast on the stationary probability distribution iff the infinite system is ergodic and converge slowly iff the infinite system is non-ergodic".

"Fast" means that the distance between the asymptotic probability distribution and the probability distribution at time $t$ decreases exponentially with time. "Slow" if the speed of convergence is slower than exponential.

share|cite|improve this question
up vote 1 down vote accepted

yes, a result in this direction was stated for a family of reversible Markov stochastic dynamics. See and the article "Ergodicity of PCA: equivalence between spatial and temporal mixing conditions" downloadable there Best.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.