Two connections between random systems and non-Gibbsian measures
  In this contribution we discuss the role disordered (or random) systems have played in the study of non-Gibbsian measures. This role has two main aspects, the distinction between which has not always been fully clear:   1) {\em From} disordered systems: Disordered systems can be used as a tool; analogies with, as well as results and methods from the study of random systems can be employed to investigate non-Gibbsian properties of a variety of measures of physical and mathematical interest.   2) {\em Of} disordered systems: Non-Gibbsianness is a property of various (joint) measures describing quenched disordered systems.   We discuss and review this distinction and a number of results related to these issues. Moreover, we discuss the mean-field version of the non-Gibbsian property, and present some ideas how a Kac limit approach might connect the finite-range and the mean-field non-Gibbsian properties. 
A.C.D. van Enter and C. Kuelske