Exchangeable, Gibbs and Equilibrium Measures for Markov Subshifts
نویسندگان
چکیده
We study a class of strongly irreducible, multidimensional, topological Markov shifts, comparing two notions of “symmetric measure”: exchangeability and the Gibbs property. We show that equilibrium measures for such shifts (unique and weak Bernoulli in the one dimensional case) exhibit a variety of spectral properties.
منابع مشابه
Gibbs and Equilibrium Measures for Some Families of Subshifts
For SFTs, any equilibrium measure is Gibbs, as long a f has dsummable variation. This is a theorem of Lanford and Ruelle. Conversely, a theorem of Dobrušin states that for strongly-irreducible subshifts, shiftinvariant Gibbs-measures are equilibrium measures. Here we prove a generalization of the Lanford-Ruelle theorem: for all subshifts, any equilibrium measure for a function with d-summable v...
متن کاملar X iv : m at h / 05 05 01 1 v 3 [ m at h . PR ] 8 S ep 2 00 5 EXCHANGEABLE , GIBBS AND EQUILIBRIUM MEASURES FOR MARKOV
We study a class of strongly irreducible, multidimensional, topological Markov shifts, comparing two notions of “symmetric measure”: exchangeability and the Gibbs (or conformal) property. We show that equilibrium measures for such shifts (unique and weak Bernoulli in the one dimensional case) exhibit a variety of spectral properties.
متن کاملar X iv : m at h / 05 05 01 1 v 4 [ m at h . PR ] 5 J un 2 00 6 EXCHANGEABLE , GIBBS AND EQUILIBRIUM MEASURES FOR MARKOV
We study a class of strongly irreducible, multidimensional, topological Markov shifts, comparing two notions of “symmetric measure”: exchangeability and the Gibbs (or conformal) property. We show that equilibrium measures for such shifts (unique and weak Bernoulli in the one dimensional case) exhibit a variety of spectral properties.
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