Mark Kac Seminar

February 6, 2009






Location: Utrecht, KNG80, room 130


speaker: Wioletta Ruszel and Alex Opoku (Groningen)

title: Gibbs-non-Gibbs properties for X-Y lattice and mean-field models and beyond



In this talk we will present some recent results on the study of Gibbs-non-Gibbs properties  for lattice and mean-field models.


In the first half of the talk we will present some recent results on the preservation, loss and recovery of Gibbsianness for the X-Y lattice model. On the topic of preservation we will present results for a more general class of lattice models, subjected to various transformations.


In the second half we will present various corresponding results for mean-field models.



speaker: Federico Camia (VU Amsterdam)

title: Ising (Conformal) Fields and Cluster Area Measures


I will discuss a representation for the magnetization field of the critical two-dimensional Ising model in the scaling limit as a (conformal) random field using renormalized area measures associated with SLE (Schramm-Loewner Evolution) clusters.
The renormalized areas come from the scaling limit of critical FK (Fortuin-Kasteleyn) clusters and the random field is a convergent sum of the area measures with random signs.
The representation is based on the lattice interpretation of the magnetization as the sum of the signed "areas" of clusters.

If time permits, extensions to off-critical scaling limits, to three dimensions and to Potts models will also be discussed.

The talk will be based on joint work with C. Newman (arXiv:0812.4030) and on work in progress with C. Garban and Newman.
No knowledge of conformal field theory is needed.


Mark Kac Seminar 2008-2009


last updated: 18 dec 2008by Markus