Projections of Gibbs States for Hölder Potentials

Mark Stephens Piraino

doi:10.1007/s10955-018-1967-3

Projections of Gibbs States for Hölder Potentials

Mark Stephens Piraino^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	952-961
Number of pages	10
Journal	Journal of Statistical Physics
Volume	170
Issue number	5
DOIs	https://doi.org/10.1007/s10955-018-1967-3
State	Published - Mar 1 2018

Keywords

Hidden Markov measures
Hilbert’s metric
Projections of Gibbs states

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-018-1967-3

Cite this

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title = "Projections of Gibbs States for H{\"o}lder Potentials",

abstract = "We give a short proof that the projection of a Gibbs state for a H{\"o}lder continuous potential on a mixing shift of finite type under a 1-block fiber-wise mixing factor map has a H{\"o}lder 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.",

keywords = "Hidden Markov measures, Hilbert{\textquoteright}s metric, Projections of Gibbs states",

author = "Piraino, {Mark Stephens}",

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AB - 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.

KW - Hidden Markov measures

KW - Hilbert’s metric

KW - Projections of Gibbs states

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JF - Journal of Statistical Physics

IS - 5

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Projections of Gibbs States for Hölder Potentials

Abstract

Keywords

ASJC Scopus subject areas

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