English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We extend the notion of Gibbsianness for mean-field systems to the set-up ofgeneral (possibly continuous) local state spaces. We investigate the Gibbsproperties of systems arising from an initial mean-field Gibbs measure byapplication of given local transition kernels. This generalizes previouscase-studies made for spins taking finitely many values to the first step indirection to a general theory, containing the following parts: (1) A formulafor the limiting conditional probability distributions of the transformedsystem. It holds both in the Gibbs and non-Gibbs regime and invokes aminimization problem for a "constrained rate-function". (2) A criterion forGibbsianness of the transformed system for initial Lipschitz-Hamiltoniansinvolving concentration properties of the transition kernels. (3) A continuityestimate for the single-site conditional distributions of the transformedsystem. While (2) and (3) have provable lattice-counterparts, thecharacterization of (1) is stronger in mean-field. As applications we showshort-time Gibbsianness of rotator mean-field models on the (q-1)-dimensionalsphere under diffusive time-evolution and the preservation of Gibbsiannessunder local coarse-graining of the initial local spin space.

Continuous Spin Mean-Field models: Limiting kernels and Gibbs Properties of local transforms