## Samenvatting

We extend the notion of Gibbsianness for mean-field systems to the setup of general (possibly continuous) local state spaces. We investigate the Gibbs properties of systems arising from an initial mean-field Gibbs measure by application of given local transition kernels. This generalizes previous case studies made for spins taking finitely many values to the first step in the direction to a general theory containing the following parts: (1) A formula for the limiting conditional probability distributions of the transformed system (it holds both in the Gibbs and in the non-Gibbs regime and invokes a minimization problem for a "constrained rate function"), (2) a criterion for Gibbsianness of the transformed system for initial Lipschitz-Hamiltonians involving concentration properties of the transition kernels, and (3) a continuity estimate for the single-site conditional distributions of the transformed system. While (2) and (3) have provable lattice counterparts, the characterization of (1) is stronger in mean field. As applications we show short-time Gibbsianness of rotator mean-field models on the (q-1)-dimensional sphere under diffusive time evolution and the preservation of Gibbsianness under local coarse graining of the initial local spin space.

Originele taal-2 | English |
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Artikelnummer | 125215 |

Aantal pagina's | 31 |

Tijdschrift | Journal of Mathematical Physics |

Volume | 49 |

Nummer van het tijdschrift | 12 |

DOI's | |

Status | Published - dec.-2008 |