Roberto Fernández

Mathematical Institute, University of Utrecht

"Gibbs-non-Gibbs dynamical transition: a large-deviation paradigm"

Alan contributed decisively to the large paper with Aernout van Enter and myself dealing with non-Gibbsianness as a result of renormalization transformations. Fifteen years later, the same mathematical techniques led to the observation that low-temperature Ising measures subjected to a high-temperature spin-flip evolution can become non-Gibbsian after a finite time. I will report on a new paradigm for this type of evolutions, in which Gibbs-non-Gibbs transitions are related to changes in the large-deviation rates of conditioned evolutions of measures: Rates with multiple global minima lead to non-Gibbsianness. I will present the main ideas behind this new approach and report on rigorous results for mean-field and local mean-field models. Work in collaboration with F. den Hollander (Leiden) and J. Martinez (Buenos Aires)