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The Posterior metric and the Goodness of Gibbsianness for transforms of Gibbs measures


 
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1. Title Title of document The Posterior metric and the Goodness of Gibbsianness for transforms of Gibbs measures
 
2. Creator Author's name, affiliation, country Christof Külske; University of Groningen
 
2. Creator Author's name, affiliation, country Alex A Opoku; University of Groningen
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Time-evolved Gibbs measures, non-Gibbsian measures: Dobrushin uniqueness; phase transitions; specification; posterior metric
 
3. Subject Subject classification 60K35; 82B20; 82B26
 
4. Description Abstract We present a general method to derive continuity estimates for conditional probabilities of general (possibly continuous) spin models subjected to local transformations. Such systems arise in the study of a stochastic time-evolution of Gibbs measures or as noisy observations. Assuming no a priori metric on the local state spaces but only a measurable structure, we define the posterior metric on the local image space. We show that it allows in a natural way to divide the local part of the continuity estimates from the spatial part (which is treated by Dobrushin uniqueness here). We show in the concrete example of the time evolution of rotators on the $(q-1)$-dimensional sphere how this method can be used to obtain estimates in terms of the familiar Euclidean metric. In another application we prove the preservation of Gibbsianness for sufficiently fine local coarse-grainings when the Hamiltonian satisfies a Lipschitz property
 
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7. Date (YYYY-MM-DD) 2008-07-17
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/560
 
10. Identifier Digital Object Identifier 10.1214/EJP.v13-560
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 13
 
12. Language English=en
 
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