Dimers and circle patterns
| Autor: | Kenyon, Richard, Lam, Wai Yeung, Ramassamy, Sanjay, Russkikh, Marianna |
|---|---|
| Přispěvatelé: | Department of Mathematics [Yale University], Yale University [New Haven], Department of Mathematics, Brown University, Brown University, Département de Mathématiques et Applications - ENS Paris (DMA), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Centre National de la Recherche Scientifique (CNRS), Université Paris sciences et lettres (PSL), Université de Genève (UNIGE), NSF grant DMS-1713033, Simons Foundation award 327929, Fondation Simone et Cino del Duca, Chaire ENS-MHI, Fondation Sciences Mathématiques de Paris, NCCR SwissMAP of the SNSF, ANR-18-CE40-0033,DIMERS,Dimères : de la combinatoire à la mécanique quantique(2018), European Project: 340340,EC:FP7:ERC,ERC-2013-ADG,COMPASP(2014), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Université de Genève = University of Geneva (UNIGE), École normale supérieure - Paris (ENS Paris) |
| Rok vydání: | 2022 |
| Předmět: |
Mathematics - Complex Variables
52C26 82B20 General Mathematics [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] FOS: Physical sciences Geometric Topology (math.GT) [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV] Mathematical Physics (math-ph) Dynamical Systems (math.DS) Mathematics - Geometric Topology [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] FOS: Mathematics Mathematics - Dynamical Systems Complex Variables (math.CV) Mathematical Physics |
| Zdroj: | Annales Scientifiques de l'École Normale Supérieure Annales Scientifiques de l'École Normale Supérieure, Société mathématique de France, In press Annales Scientifiques de l'École Normale Supérieure, 2022, 55 (3), pp.863-901. ⟨10.24033/asens.2507⟩ Annales Scientifiques de l'École Normale Supérieure, Société mathématique de France, 2022, 55 (3), pp.863-901. ⟨10.48550/arXiv.1810.05616⟩ |
| ISSN: | 1873-2151 0012-9593 |
| Popis: | We establish a correspondence between the dimer model on a bipartite graph and a circle pattern with the combinatorics of that graph, which holds for graphs that are either planar or embedded on the torus. The set of positive face weights on the graph gives a set of global coordinates on the space of circle patterns with embedded dual. Under this correspondence, which extends the previously known isoradial case, the urban renewal (local move for dimer models) is equivalent to the Miquel move (local move for circle patterns). As a consequence the Miquel dynamics on circle patterns is governed by the octahedron recurrence. As special cases of these circle pattern embeddings, we recover harmonic embeddings for resistor networks and s-embeddings for the Ising model. Comment: 39 pages, 13 figures. To appear in Annales scientifiques de l'\'Ecole normale sup\'erieure |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|