Abstract:
It is known that simple renormalization transformation of Gibbs
measures (states) can produce non-Gibssian measures.
The hypothesis about the necessary and sufficient conditions for
preservation of Gibbsianity - the so-called absence of the hidden
phase-transitions, was proposed in 1993. I will discuss a novel
interpretation of the hidden phase-transition scenario and some
recent progress towards the proof.
In the second part of the talk, I will discuss certain aspects of
the Dobrushin reconstruction program for the renormalized Gibbs
states (which may or may not be Gibbs). In particular, I will show
that a generalized variational principle holds.
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