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A random tiling model for two dimensional electrostatics


About this Title

Mihai Ciucu

Publication: Memoirs of the American Mathematical Society
Publication Year 2005: Volume 178, Number 839
ISBNs: 978-0-8218-3794-8 (print); 978-1-4704-0440-6 (online)
DOI: http://dx.doi.org/10.1090/memo/0839
MathSciNet review: 2172582
MSC (2000): Primary 82B23; Secondary 05A15, 05A16, 05B40, 60C05, 60D05, 60F99, 82B44

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Table of Contents


Chapters

  • A random tiling model for two dimensional electrostatics
  • 1. Introduction
  • 2. Definitions, statement of results and physical interpretation
  • 3. Reduction to boundary-influenced correlations
  • 4. A simple product formula for correlations along the boundary
  • 5. A -fold sum for
  • 6. Separation of the -fold sum for in terms of -fold integrals
  • 7. The asymptotics of the 's and 's
  • 8. Replacement of the 's and 's by their asymptotics
  • 9. Proof of Proposition 7.2
  • 10. The asymptotics of a multidimensional Laplace integral
  • 11. The asymptotics of . Proof of Theorem 2.2
  • 12. Another simple product formula for correlations along the boundary
  • 13. The asymptotics of . Proof of Theorem 2.1
  • 14. A conjectured general two dimensional superposition principle
  • 15. Three dimensions and concluding remarks
  • B. Plane partitions I: A generalization of MacMahon's formula
  • 1. Introduction
  • 2. Two families of regions
  • 3. Reduction to simply-connected regions
  • 4. Recurrences for and
  • 5. Proof of Proposition 2.1
  • 6. The guessing of and