A random tiling model for two dimensional electrostatics

DOI10.1090/memo/0839zbMath1148.82009arXivmath-ph/0303067OpenAlexW2021702363MaRDI QIDQ5713279

Mihai Ciucu

Publication date: 13 December 2005

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0303067

zbMATH Keywords

correlationscaling limitasymptotic enumerationrandom tilingselectrostaticsexact enumerationperfect matchingsplane partitionslozenge tilingsdimer modelsimple product formulas

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Exact enumeration problems, generating functions (05A15) Combinatorial probability (60C05) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Exactly solvable models; Bethe ansatz (82B23) Asymptotic enumeration (05A16) Combinatorial aspects of packing and covering (05B40) Limit theorems in probability theory (60F99)

Related Items (18)

Macroscopically separated gaps in dimer coverings of Aztec rectangles ⋮ The weak Lefschetz property for monomial ideals of small type ⋮ Symmetries of shamrocks. II: Axial shamrocks ⋮ Interactions between interleaving holes in a sea of unit rhombi ⋮ Hitting matrix and domino tiling with diagonal impurities ⋮ Lozenge tilings of hexagons with removed core and satellites ⋮ Gaps in dimer systems on doubly periodic planar bipartite graphs ⋮ The interaction of a gap with a free boundary in a two dimensional dimer system ⋮ Tilings of hexagons with a removed triad of bowties ⋮ Signed lozenge tilings ⋮ Three interactions of holes in two dimensional dimer systems ⋮ Lozenge tilings with gaps in a \(90\degree\) wedge domain with mixed boundary conditions ⋮ The emergence of the electrostatic field as a Feynman sum in random tilings with holes ⋮ A bijection theorem for domino tilings with diagonal impurities ⋮ The interaction of collinear gaps of arbitrary charge in a two dimensional dimer system ⋮ Correlation of a macroscopic dent in a wedge with mixed boundary conditions ⋮ Lozenge tilings of doubly-intruded hexagons ⋮ The effect of microscopic gap displacement on the correlation of gaps in dimer systems

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