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Planar dimers and Harnack curves
, 2003
"... 1.1 Summary of results In this paper we study the connection between dimers and Harnack curves discovered in [12]. To any periodic edgeweighted planar bipartite graph Γ ..."
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Cited by 32 (6 self)
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1.1 Summary of results In this paper we study the connection between dimers and Harnack curves discovered in [12]. To any periodic edgeweighted planar bipartite graph Γ
Lectures on dimers
 In Statistical mechanics, volume 16 of IAS/Park City Math. Ser
, 2009
"... ar ..."
Quiver gauge theories at resolved and deformed singularities using dimers
 JHEP
"... The gauge theory on a set of D3branes at a toric CalabiYau singularity can be encoded in a tiling of the 2torus denoted dimer diagram (or brane tiling). We use these techniques to describe the effect on the gauge theory of geometric operations partially smoothing the singularity at which D3brane ..."
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Cited by 21 (3 self)
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The gauge theory on a set of D3branes at a toric CalabiYau singularity can be encoded in a tiling of the 2torus denoted dimer diagram (or brane tiling). We use these techniques to describe the effect on the gauge theory of geometric operations partially smoothing the singularity at which D3branes sit, namely partial resolutions and complex deformations. More specifically, we describe the effect of arbitrary partial resolutions, including those which split the original singularity into two separated. The gauge theory correspondingly splits into two sectors (associated to branes in either singularity) decoupled at the level of massless states. We also describe the effect of complex deformations, associated to geometric transitions triggered by the presence of fractional branes with confinement in their infrared. We provide tools to The study of the N = 1 supersymmetric gauge theory on a stack of D3branes probing a CalabiYau threefold conical singularity is a fruitful source of new insights into brane dynamics [1, 2], the AdS/CFT correspondence [3], and its extensions to nonconformal situations by the addition of fractional branes [4].
Discrete complex analysis and probability
 PROC. INT. CONGRESS OF MATHEMATICIANS (ICM) (HYDERABAD, INDIA) PP 565–621 (ARXIV:1009.6077
, 2010
"... We discuss possible discretizations of complex analysis and some of their applications to probability and mathematical physics, following our recent work with Dmitry Chelkak, Hugo DuminilCopin and Clément Hongler. ..."
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Cited by 16 (1 self)
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We discuss possible discretizations of complex analysis and some of their applications to probability and mathematical physics, following our recent work with Dmitry Chelkak, Hugo DuminilCopin and Clément Hongler.
Brane tilings and exceptional collections
 Trans. Moscow Math. Soc
, 1963
"... hepth/0602041 ..."
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Relating Field Theories via Stochastic Quantization
, 903
"... This note aims to subsume several apparently unrelated models under a common framework. Several examples of well–known quantum field theories are listed which are connected via stochastic quantization. We highlight the fact that the quantization method used to obtain the quantum crystal is a discret ..."
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This note aims to subsume several apparently unrelated models under a common framework. Several examples of well–known quantum field theories are listed which are connected via stochastic quantization. We highlight the fact that the quantization method used to obtain the quantum crystal is a discrete analog of stochastic quantization. This model is of interest for string theory, since the (classical) melting crystal corner is related to the topological A–model. We outline several ideas for interpreting the quantum crystal on the string theory side of the correspondence, exploring interpretations in the Wheeler–De Witt framework and in terms of a non–Lorentz invariant limit of topological M–theory. Contents
INHOMOGENEOUS BOND PERCOLATION ON SQUARE, TRIANGULAR, AND HEXAGONAL LATTICES
 SUBMITTED TO THE ANNALS OF PROBABILITY
, 2011
"... The star–triangle transformation is used to obtain an equivalence extending over the set of all (in)homogeneous bond percolation models on the square, triangular, and hexagonal lattices. Amongst the consequences are boxcrossing (RSW) inequalities for such models with parametervalues at which the t ..."
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Cited by 9 (3 self)
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The star–triangle transformation is used to obtain an equivalence extending over the set of all (in)homogeneous bond percolation models on the square, triangular, and hexagonal lattices. Amongst the consequences are boxcrossing (RSW) inequalities for such models with parametervalues at which the transformation is valid. This is a step towards proving the universality and conformality of these processes. It implies criticality of such values, thereby providing a new proof of the critical point of inhomogeneous systems. The proofs extend to certain isoradial models to which previous methods do not apply.