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memo_has_moved_text(); A random tiling model for two dimensional electrostatics

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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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 $(2m + 2n)$-fold sum for $\omega _b$
• 6. Separation of the $(2m + 2n)$-fold sum for $\omega _b$ in terms of $4mn$-fold integrals
• 7. The asymptotics of the $T^{(n)}$'s and $T'^{(n)}$'s
• 8. Replacement of the $T^{(k)}$'s and $T'^{(k)}$'s by their asymptotics
• 9. Proof of Proposition 7.2
• 10. The asymptotics of a multidimensional Laplace integral
• 11. The asymptotics of $\omega _b$. Proof of Theorem 2.2
• 12. Another simple product formula for correlations along the boundary
• 13. The asymptotics of $\bar {\omega }_b$. 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 $\mathrm {M}(R_{\mathbf {l}, \mathbf {q}}(x))$ and $\mathrm {M}(\bar {R}_{\mathbf {l}, \mathbf {q}}(x))$
• 5. Proof of Proposition 2.1
• 6. The guessing of $\mathrm {M}(R_{\mathbf {l}, \mathbf {q}}(x))$ and $\mathrm {M}(\bar {R}_{\mathbf {l}, \mathbf {q}}(x))$