Conformal invariance of dimer heights on isoradial double graphs
Annales de l’Institut Henri Poincaré D, Tome 4 (2017) no. 3, pp. 273-307.

An isoradial graph is a planar graph in which each face is inscribable into a circle of common radius. We study the 2-dimensional perfect matchings on a bipartite isoradial graph, obtained from the union of an isoradial graph and its interior dual graph. Using the isoradial graph to approximate a simply-connected domain bounded by a simple closed curve, by letting the mesh size go to zero, we prove that in the scaling limit, the distribution of height is conformally invariant and converges to a Gaussian free �field.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/41
Classification : 82-XX, 30-XX, 60-XX
Mots-clés : Dimer model, perfect matching, conformal invariance, Gaussian free field, isoradial graph 
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     author = {Li, Zhongyang},
     title = {Conformal invariance of dimer heights on isoradial double graphs},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {273--307},
     volume = {4},
     number = {3},
     year = {2017},
     doi = {10.4171/aihpd/41},
     mrnumber = {3713018},
     zbl = {1377.82019},
     language = {en},
     url = {http://archive.numdam.org/articles/10.4171/aihpd/41/}
}
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Li, Zhongyang. Conformal invariance of dimer heights on isoradial double graphs. Annales de l’Institut Henri Poincaré D, Tome 4 (2017) no. 3, pp. 273-307. doi : 10.4171/aihpd/41. http://archive.numdam.org/articles/10.4171/aihpd/41/

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