Displaying similar documents to “An ergodic theorem for a class of spin systems”

Operators with an ergodic power

Teresa Bermúdez, Manuel González, Mostafa Mbekhta (2000)

Studia Mathematica

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We prove that if some power of an operator is ergodic, then the operator itself is ergodic. The converse is not true.

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

M. Courbage, D. Hamdan (2001)

Colloquium Mathematicae

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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.

Multiparameter pointwise ergodic theorems for Markov operators on L.

Ryotaro Sato (1994)

Publicacions Matemàtiques

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Let P1, ..., Pd be commuting Markov operators on L∞(X,F,μ), where (X,F,μ) is a probability measure space. Assuming that each Pi is either conservative or invertible, we prove that for every f in Lp(X,F,μ) with 1 ≤ p < ∞ the averages Anf = (n + 1)-d Σ0≤ni≤n P1