Transformations of One-Dimensional Gibbs Measures with Infinite Range Interaction

#### F. Redig, F. Wang

2010, v.16, №4, 737-752

ABSTRACT

We study single-site stochastic and deterministic transformations 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.

Keywords: Gibbs measures,potential,Kozlov theorem,house-of-cards coupling,renormalization group transformation