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Non-Gibbsian measures on the lattice, in mean-field and in between

Mathematical Physics & Probability

Speaker: Christof Kuelske, University of Groningen
Location: 1147 MSB
Start time: Wed, Nov 15 2006, 2:10PM

Many examples of seemingly harmless transformations of lattice spin measures in mathematical statistical mechanics are known to destroy the Gibbs property. This is caused by the emergence of non-localities in the joint measure. Less known, corresponding phenomena also exist for mean-field (exchangeable)  systems, with a suitable notion of mean-field Gibbsianness.  We describe results for this in both lattice and mean field models, focussing on  stochastic time-evolutions for which non-Gibbsianness was only recently discovered.  We also discuss the relation to disordered systems and large deviations,  and conjecture how lattice and mean-field results may be linked  by a Kac-(long range-) limit. Joint work with: A.C.D. van Enter,  A. Le Ny,  A. Opoku, F. Redig.