On the prevalence of non-Gibbsian states in mathematical physics

Abstract

Gibbs measures are the main object of study in equilibrium statistical mechanics, and are used in many other contexts, including dynamical systems and ergodic theory, and spatial statistics. However, in a large number of natural instances one encounters measures that are not of Gibbsian form. We present here a number of examples of such non-Gibbsian measures, and discuss some of the underlying mathematical and physical issues to which they gave rise