Conformal invariance and universality of the dimer model

Diplôme Thèse Conformal invariance and universality of the dimer model eng 2019-05-20 author Russkikh Marianna 804248 director Smirnov Stanislav 135274 director Chelkak Dmitry 651589 10.13097/archive-ouverte/unige:119698 urn:nbn:ch:unige-1196981 Sc. 5344 This thesis is dedicated to the study of the conformal invariance and the universality of the dimer model on planar bipartite graphs. Kenyon [41, 42] has established the conformal invariance of the limiting distribution of the dimer height function in the case of Temperleyan discretizations, discrete domains on the square lattice with special boundary conditions. In the thesis, we extended Kenyon's result for more general classes of approximations on the square lattice. Yet another direction of research in the dimer model is the universality (which means that the scaling limit is independent of the shape of the lattice) of the planar dimer model. We describe how to construct a circle pattern embedding of a dimer planar graph using its Kasteleyn weights. We also introduce the definition of discrete holomorphicity on such an embedding. We focus on understanding the link between these functions and actual continuous holomorphic functions to study holomorphic observables of the dimer model. Dewey 510 25 Section de mathématiques 11 false 794a9136-8368-4321-8e70-b1b28f95eba1 Thesis Public diser.pdf 3935895 application/pdf openAccess Faculté des sciences / Section de mathématiques

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Conformal invariance and universality of the dimer model				2019	848	397

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Russkikh, Marianna