Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

On the directional entropy of ℤ²-actions generated by cellular automata

100%

Courbage M., Kamiński B.

Studia Mathematica

2002

tom 153

nr 3

285-295

We show that for any cellular automaton (CA) ℤ²-action Φ on the space of all doubly infinite sequences with values in a finite set A, determined by an automaton rule $F = F_{[l,r]}$, l,r ∈ ℤ, l ≤ r, and any Φ-invariant Borel probability measure, the directional entropy $h_{v⃗}(Φ)$, v⃗= (x,y) ∈ ℝ², is bounded above by $max(|z_{l}|,|z_{r}|) log #A$ if $z_{l}z_{r} ≥ 0$ and by $|z_{r} - z_{l}|$ in the opposite case, where $z_{l} = x + ly$, $z_{r} = x + ry$. We also show that in the class of permutative CA-actions the bounds are attained if the measure considered is uniform Bernoulli.

A family of stationary processes with infinite memory having the same p-marginals. Ergodic and spectral properties

100%

Courbage M., Hamdan D.

Colloquium Mathematicum

2001

tom 90

nr 2

159-179

We construct a large family of ergodic non-Markovian processes with infinite memory having the same p-dimensional marginal laws of an arbitrary ergodic Markov chain or projection of Markov chains. Some of their spectral and mixing properties are given. We show that the Chapman-Kolmogorov equation for the ergodic transition matrix is generically satisfied by infinite memory processes.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Studia Mathematica

2 Courbage M.

1 Hamdan D.

1 Kamiński B.

1 2002

1 2001

Wyniki wyszukiwania

On the directional entropy of ℤ²-actions generated by cellular automata

A family of stationary processes with infinite memory having the same p-marginals. Ergodic and spectral properties