Transformations of one-dimensional Gibbs measures with infinite range interaction

Details Transformations of one-dimensional Gibbs measures with infinite range interaction Transformations of one-dimensional Gibbs measures with infinite range interaction

2010-02-25

arxiv.org/abs/1002.4796v1

Markov Proc. Rel. Fields, 16, pp. 737-752, 2010

Mathematics

Probability

Scientific paper

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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