Geodesic
Dominos in hedgehog domains
Annales de l’Institut Henri Poincaré D, Tome 8 (2021) no. 1, pp. 1-33.

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We introduce a new class of discrete approximations of planar domains that we call “hedgehog domains”. In particular, this class of approximations contains two-step Aztec diamonds and similar shapes. We show that fluctuations of the height function of a random dimer tiling on hedgehog discretizations of a planar domain converge in the scaling limit to the Gaussian Free Field with Dirichlet boundary conditions. Interestingly enough, in this case the dimer model coupling function satisfies the same Riemann-type boundary conditions as fermionic observables in the Ising model.

In addition, using the same factorization of the double-dimer model coupling function as in [18], we show that in the case of approximations by hedgehog domains the expectation of the double-dimer height function is harmonic in the scaling limit.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/96
Classification : 60-XX
Keywords: Lattice models, Dimer model, height function, GFF 
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Russkikh, Marianna. Dominos in hedgehog domains. Annales de l’Institut Henri Poincaré D, Tome 8 (2021) no. 1, pp. 1-33. doi : 10.4171/aihpd/96. http://geodesic.mathdoc.fr/articles/10.4171/aihpd/96/

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