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Dimer model and holomorphic functions on t-embeddings of planar graphs
dc.contributor.authorChelkak, Dmitry
dc.contributor.authorLaslier, Benoît
dc.contributor.authorRusskikh, Marianna
dc.date.accessioned2023-06-01T20:48:23Z
dc.date.available2024-06-01 16:48:21en
dc.date.available2023-06-01T20:48:23Z
dc.date.issued2023-05
dc.identifier.citationChelkak, Dmitry; Laslier, Benoît ; Russkikh, Marianna (2023). "Dimer model and holomorphic functions on t- embeddings of planar graphs." Proceedings of the London Mathematical Society 126(5): 1656-1739.
dc.identifier.issn0024-6115
dc.identifier.issn1460-244X
dc.identifier.urihttps://hdl.handle.net/2027.42/176820
dc.description.abstractWe introduce the framework of discrete holomorphic functions on t-embeddings of weighted bipartite planar graphs; t-embeddings also appeared under the name Coulomb gauges in a recent paper (Kenyon, Lam, Ramassamy, and Russkikh, Dimers and circle patterns, 2018). We argue that this framework is particularly relevant for the analysis of scaling limits of the height fluctuations in the corresponding dimer models. In particular, it unifies both Kenyon’s interpretation of dimer observables as derivatives of harmonic functions on T-graphs and the notion of s-holomorphic functions originated in Smirnov’s work on the critical Ising model. We develop an a priori regularity theory for such functions and provide a meta-theorem on convergence of the height fluctuations to the Gaussian Free Field. We also discuss how several more standard discretizations of complex analysis fit this general framework.
dc.publisherWorld Sci. Publ
dc.publisherWiley Periodicals, Inc.
dc.titleDimer model and holomorphic functions on t-embeddings of planar graphs
dc.typeArticle
dc.rights.robotsIndexNoFollow
dc.subject.hlbsecondlevelMathematics
dc.subject.hlbtoplevelScience
dc.description.peerreviewedPeer Reviewed
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/176820/1/plms12516.pdf
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/176820/2/plms12516_am.pdf
dc.identifier.doi10.1112/plms.12516
dc.identifier.sourceProceedings of the London Mathematical Society
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dc.working.doiNOen
dc.owningcollnameInterdisciplinary and Peer-Reviewed


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