Projections of Gibbs States for Hölder Potentials

Abstract

In this paper we give a short proof that the projection of a Gibbs state for a Hölder continuous potential on a mixing shift of finite type under a 1-block fiber-wise mixing factor map has a Hölder continuous g function. This improves a number of previous results. The key insight in the proof is to realize the measure of a cylinder set in terms of positive operators and use cone techniques.

11 pages. V2: small changes, corrected some references

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