# A random tiling model for two dimensional electrostatics [electronic resource] / Mihai Ciucu

- Author:
- Ciucu, Mihai, 1968-
- Published:
- Providence, R.I. : American Mathematical Society, 2005.
- Physical Description:
- 1 online resource (ix, 144 pages : illustrations)
- Access Online:
- ezaccess.libraries.psu.edu

ezaccess.libraries.psu.edu

- Series:
- Memoirs of the American Mathematical Society, 0065-9266 (print), 1947-6221 (online); v. 839
- Restrictions on Access:
- Access is restricted to licensed institutions
- Contents:
- 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 $\mathrm {M}(\bar {R}_{\mathbf {l}, \mathbf {q}}(x))$
- Subject(s):
- ISBN:
- 9781470404406 (online)
- Note:
- "Volume 178, number 839 (third of 5 numbers)."

AVAILABLE ONLINE TO AUTHORIZED PSU USERS. - Bibliography Note:
- Includes bibliographical references (page 144).
- Reproduction Note:
- Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012
- Technical Details:
- Mode of access : World Wide Web

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