Journée-séminaire de combinatoire

(équipe CALIN du LIPN, université Paris-Nord, Villetaneuse)

Le 22 octobre 2019 à 14h50 en Amphi Darwin, Andrea Sportiello nous parlera de : The tangent method for the determination of Arctic curves: the simplest rigorous application

Résumé : In the paper Arctic curves of the six-vertex model on generic domains: the Tangent Method [J. Stat. Phys. 164 (2016), arXiv:1605.01388], of Filippo Colomo and myself, we pose the basis for a method aimed at the determination of the ``arctic curve'' of large random combinatorial structures, i.e. the boundary between regions with zero and non-zero local entropy, in the scaling limit. In this paper many things are claimed, and few are proven. In particular, it is not made clear that variants of it can be made fully rigorous in certain circumstances. In this seminar we present the simplest such instance: we rederive the arctic circle phenomenon for ``domino tilings of the aztec diamond'', first discovered by Jockusch, Propp and Shor [arXiv:math/9801068, but in fact from 1995].

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