Gibbs Properties of the Fuzzy Potts Model on Trees and in Mean Field

O. Häggström; C. Külske

Gibbs Properties of the Fuzzy Potts Model on Trees and in Mean Field

O. Häggström, C. Külske

Probability and Statistics

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We study Gibbs properties of the fuzzy Potts model in the mean field case (i.e. on a complete graph) and on trees. For the mean field case, a complete characterization of the set of temperatures for which non-Gibbsianness happens is given. The results for trees are somewhat less explicit, but we do show for general trees that non-Gibbsianness of the fuzzy Potts model happens exactly for those temperatures where the underlying Potts model has multiple Gibbs measures.

Originele taal-2	English
Pagina's (van-tot)	477-506
Aantal pagina's	30
Tijdschrift	Markov Processes and Related Fields
Volume	10
Status	Published - 2004

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title = "Gibbs Properties of the Fuzzy Potts Model on Trees and in Mean Field",

abstract = "We study Gibbs properties of the fuzzy Potts model in the mean field case (i.e. on a complete graph) and on trees. For the mean field case, a complete characterization of the set of temperatures for which non-Gibbsianness happens is given. The results for trees are somewhat less explicit, but we do show for general trees that non-Gibbsianness of the fuzzy Potts model happens exactly for those temperatures where the underlying Potts model has multiple Gibbs measures.",

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author = "O. H{\"a}ggstr{\"o}m and C. K{\"u}lske",

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T1 - Gibbs Properties of the Fuzzy Potts Model on Trees and in Mean Field

AU - Häggström, O.

AU - Külske, C.

N1 - Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen. Research Institute for Mathematics and Computing Science (IWI)

PY - 2004

Y1 - 2004

N2 - We study Gibbs properties of the fuzzy Potts model in the mean field case (i.e. on a complete graph) and on trees. For the mean field case, a complete characterization of the set of temperatures for which non-Gibbsianness happens is given. The results for trees are somewhat less explicit, but we do show for general trees that non-Gibbsianness of the fuzzy Potts model happens exactly for those temperatures where the underlying Potts model has multiple Gibbs measures.

AB - We study Gibbs properties of the fuzzy Potts model in the mean field case (i.e. on a complete graph) and on trees. For the mean field case, a complete characterization of the set of temperatures for which non-Gibbsianness happens is given. The results for trees are somewhat less explicit, but we do show for general trees that non-Gibbsianness of the fuzzy Potts model happens exactly for those temperatures where the underlying Potts model has multiple Gibbs measures.

KW - mean-field models

KW - trees

KW - non-Gibbsian measures

KW - Gibbs measures

KW - fuzzy Potts model

KW - Potts model

M3 - Article

SN - 1024-2953

VL - 10

SP - 477

EP - 506

JO - Markov Processes and Related Fields

JF - Markov Processes and Related Fields

ER -

Gibbs Properties of the Fuzzy Potts Model on Trees and in Mean Field

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