Starts 5 Feb 2008 12:30
Ends 5 Feb 2008 20:00
Central European Time
SISSA, Lecture Room 'D'
The Arctic Circle Theorem (Jockusch-Propp-Shor) concerns a model of domino tiling with peculiar boundary conditions, exhibiting phase separation, with the emergence of `limit shapes' and `arctic curves'. The computation of such objects, and the characterization of their fluctuations, has been performed for several other models (Propp, Kenyon, Reshetikhin, Okounkov), with deep implication in algebraic combinatorics and algebraic geometry. However all such models can be viewed as models of dimers, i.e. of discrete free fermions. The most natural generalization of such models, including an interaction, is provided by the Domain Wall Six-Vertex Model. We here derive, for this model with generic values of its parameter, the exact analytic expression of the arctic curves, and characterize their fluctuations, thus extending the Arctic Circle Theorem beyond the dimer (free fermion) case.
  • M. Poropat