Conformal Limit for Dimer Models on the Hexagonal Lattice

Keating, David; Reshetikhin, Nicolai; Sridhar, Ananth

doi:10.1007/s10958-019-04508-2

Cited by 1 publication

(5 citation statements)

References 6 publications

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“…In Section 4 of [20] Keating Reshetikhin and Sridahrd show (in the case of the dimer models on an hexagonal lattice) that the inverse Kasteleyn away from its diagonal has a similar form. We also made this guess using numerical evidence.…”

Section: Dimer Models and Arctic Curvesmentioning

confidence: 99%

“…Now extend the first path to start at (2n − 1 − λ n + q, −s − 1 (2n−λ n +q) 2 ), with q ∈ (−∞, λ n ). See figure (20) for a diagram. Call the resulting partition function Z qs .…”

Section: Last Dual Pathmentioning

confidence: 99%

“…Our goal is going to guess the form of the inverse of the Kasteleyn matrix using numerics and an Ansatz developed by Keating, Reshetikhin and Sridahr [20]. They developed such an ansatz for the dimer model on the hexagonal lattice and we adapt their ansatz to our setting.…”

Section: Dimer Models and Arctic Curvesmentioning

confidence: 99%

“…The Ansatz [20] is that for small , as a function on pairs of vertices K −1 will act as the restriction of the function on the continuous domain R × R defined by,…”

Section: Dimer Models and Arctic Curvesmentioning

confidence: 99%

“…In this paper, we compute arctic curves for bounded lecture hall tableaux thanks to two methods: the tangent method using paths and the ansatz of [20] using dimers. Both of these methods are not fully rigorous.…”

Section: Conclusion Open Problems and Future Workmentioning

confidence: 99%

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Arctic curves phenomena for bounded lecture hall Tableaux

Corteel¹,

Keating²,

Nicoletti³

2019

Preprint

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Recently the first author and Jang Soo Kim introduced lecture hall tableaux in their study of multivariate little q-Jacobi polynomials. They then enumerated bounded lecture hall tableaux and showed that their enumeration is closely related to standard and semistandard Young tableaux. In this paper we study the asymptotic behavior of these bounded tableaux thanks to two other combinatorial models: non intersecting paths on a graph whose faces are squares and pentagons and dimer models on a lattice whose faces are hexagons and octogons. We use the tangent method to investigate the arctic curve in the model of nonintersecting lattice paths with fixed starting points and ending points distributibuted according to some arbitrary piecewise differentiable function. We then study the dimer model and use some ansatz to guess the asymptotics of the inverse of the Kasteleyn matrix confirm the arctic curve computed with the tangent method for two examples.

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Section: Dimer Models and Arctic Curvesmentioning

confidence: 99%

Section: Last Dual Pathmentioning

confidence: 99%

Section: Dimer Models and Arctic Curvesmentioning

confidence: 99%

“…The Ansatz [20] is that for small , as a function on pairs of vertices K −1 will act as the restriction of the function on the continuous domain R × R defined by,…”

Section: Dimer Models and Arctic Curvesmentioning

confidence: 99%

Section: Conclusion Open Problems and Future Workmentioning

confidence: 99%

See 3 more Smart Citations