In the first hour I will give a review of generalized Gibbs measures. Almost versus weakly Gibbsian measures are introduced: where they appear, why they are relevant, and which elements of the standard Gibbsian formalism can be exported to these classes.
In the second hour I will discuss Gibbs-non-Gibbs transitions in the framework of stochastic time evolution of Gibbs measures, and will discuss in some detail an example of diffusion of continuous spins.
After an introduction on (correlation) inequalities, I will focus on recent joint work with Olle Haggstrom and Jeff Kahn.
Our new results, concerning correlation inequalities for situations where we condition on having or not having certain connections, put earlier inequalities obtained with Jeff Kahn in a much more general framework.
They also provide new and useful extensions of results by Belitsky, Ferrari, Konno and Liggett (1997) for contact processes.