Transformations of one-dimensional Gibbs measures with infinite range interaction

preprint2010arXivOpen access

Abstract

We study single-site stochastic and deterministic transforma- tions of one-dimensional Gibbs measures in the uniqueness regime with infinite-range interactions. We prove conservation of Gibbsianness and give quantitative estimates on the decay of the transformed potential. As examples, we consider exponentially decaying potentials, and potentials decaying as a power-law.

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