Astroidal zig-zag graphs on periodic planar bipartite lattices admit explicit inverse Kasteleyn matrices by double contour integrals, yielding arctic curves, limit shapes, and convergence to Gibbs measures for periodic weightings.
Random Domino Tilings and the Arctic Circle Theorem
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
In this article we study domino tilings of a family of finite regions called Aztec diamonds. Every such tiling determines a partition of the Aztec diamond into five sub-regions; in the four outer sub-regions, every tile lines up with nearby tiles, while in the fifth, central sub-region, differently-oriented tiles co-exist side by side. We show that when n is sufficiently large, the shape of the central sub-region becomes arbitrarily close to a perfect circle of radius n/sqrt(2) for all but a negligible proportion of the tilings. Our proof uses techniques from the theory of interacting particle systems. In particular, we prove and make use of a classification of the stationary behaviors of a totally asymmetric one-dimensional exclusion process in discrete time.
verdicts
UNVERDICTED 3representative citing papers
The symmetric Dyson exclusion process exhibits ballistic scaling and non-local hydrodynamics with current j[ρ] = (1/π) sin(πρ) sinh(π H ρ) where H is the Hilbert transform, equivalent to a local two-field system, with exact solutions for block initial states matching simulations.
Proves convergence in law of random 3D dimer flows to the unique entropy-maximizing divergence-free flow and establishes corresponding large deviation principles.
citing papers explorer
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Dimer models on astroidal zig-zag graphs
Astroidal zig-zag graphs on periodic planar bipartite lattices admit explicit inverse Kasteleyn matrices by double contour integrals, yielding arctic curves, limit shapes, and convergence to Gibbs measures for periodic weightings.
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Emergent Hydrodynamics in an Exclusion Process with Long-Range Interactions
The symmetric Dyson exclusion process exhibits ballistic scaling and non-local hydrodynamics with current j[ρ] = (1/π) sin(πρ) sinh(π H ρ) where H is the Hilbert transform, equivalent to a local two-field system, with exact solutions for block initial states matching simulations.
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Large deviations for the 3D dimer model
Proves convergence in law of random 3D dimer flows to the unique entropy-maximizing divergence-free flow and establishes corresponding large deviation principles.