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dc.contributor.authorBoutillier, Cédric
dc.contributor.authorCimasoni, David
dc.contributor.authorde Tilière, Béatrice
dc.date.accessioned2020-05-04T12:53:26Z
dc.date.available2020-05-04T12:53:26Z
dc.date.issued2019
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20684
dc.language.isoenen
dc.subjectisoradial graphs
dc.subjectdimers
dc.subjectplanar graphs
dc.subjectgraphes planaires
dc.subjectgraphes isoradiaux
dc.subjectdimères
dc.subject.ddc511en
dc.titleIsoradial immersions
dc.typeDocument de travail / Working paper
dc.description.abstractenIsoradial embeddings of planar graphs play a crucial role in the study of several models of statistical mechanics, such as the Ising and dimer models. Kenyon and Schlenker give a combinatorial characterization of planar graphs admitting an isoradial embedding, and describe the space of such embeddings. In this paper we prove two results of the same type for generalizations of isoradial embeddings: isoradial immersions and minimal immersions. We show that a planar graph has a flat isoradial immersion if and only if its train-tracks do not form closed loops, and that a bipartite graph has a minimal immersion if and only if it is minimal. In both cases we describe the space of such immersions. We also give an application of our result to the bipartite dimer model defined on graphs admitting minimal immersions.
dc.publisher.cityParisen
dc.identifier.citationpages44
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphine
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-02423791
dc.subject.ddclabelPrincipes généraux des mathématiquesen
dc.description.ssrncandidatenon
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dc.description.audienceInternational
dc.date.updated2020-06-05T16:09:52Z
hal.person.labIds56663$$$506273
hal.person.labIds230390
hal.person.labIds60$$$56663


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