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Filippo Colomo |
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INFN Firenze |
Abstract
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 free fermion (dimer) case.