A.C.D.van Enter and C. Kuelske
Two connections between random systems and non-Gibbsian measures.
(83K, latex)

ABSTRACT.  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) 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) 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.