Short time conservation of Gibbsianness under local stochastic evolutions
The evolution of a Gibbs measure under a stochastic dynamics may lead to non-Gibbsian measures as opposed to standard results on high-temperature (spin-flip) Glauber dynamics. Then, any initial measure is driven exponentially fast to the unique stationary (Gibbs) measure The paper generalizes previous results for Glauber dynamics [\textit{A. C. D. van Euter}, \textit{R. Fernández}, \textit{F. den Hollander} and \textit{F. Redig}, Commun. Math. Phys. 226, No. 1, 101-130 (2002; Zbl 0990.82018)]. It is proved that a Gibbs measure with a finite range interaction, evolving under a general reversible local stochastic dynamics, remains Gibbsian for a short interval of time.
scientific article; zbMATH DE number 1879674