Sharp thresholds for Gibbs-non-Gibbs transition in the fuzzy Potts models with a Kac-type interaction
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Date
2015
Authors
Volume
2087
Issue
Journal
Series Titel
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Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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Abstract
We investigate the Gibbs properties of the fuzzy Potts model on the $d$-dimensional torus with Kac interaction. We use a variational approach for profiles inspired by that of Fernández, den Hollander and Martínez citeFeHoMa14 for their study of the Gibbs-non-Gibbs transitions of a dynamical Kac-Ising model on the torus. As our main result, we show that the mean-field thresholds dividing Gibbsian from non-Gibbsian behavior are sharp in the fuzzy Kac-Potts model. On the way to this result we prove a large deviation principle for color profiles with diluted total mass densities and use monotocity arguments
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Keywords
Potts models, Kac model, fuzzy Lac-Potts model, Gibbs versus non-Gibbs, large deviation principles, diluted large deviation principles
Citation
Jahnel, B., & Külske, C. (2015). Sharp thresholds for Gibbs-non-Gibbs transition in the fuzzy Potts models with a Kac-type interaction (Vol. 2087). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.