A Random Tiling Model for Two-Dimensional Electrostatics
| Author/creator | Ciucu, Mihai, 1968- Author |
| Format | Electronic |
| Publication Info | Providence : American Mathematical Society |
| Description | 144 p. ill |
| Supplemental Content | Full text available from Ebook Central - Academic Complete |
| Supplemental Content | Full text available from Memoirs of the American Mathematical Society - Backfile |
| Subjects |
| Series | Memoirs of the American Mathematical Society Ser. 178 |
| Summary | Annotation Part A. A Random Tiling Model for Two Dimensional Electrostatics: Introduction Definitions, statement of results and physical interpretation Reduction to boundary-influenced correlations A simple product formula for correlations along the boundary A $(2m+2n)$-fold sum for $\omega_b$ Separation of the $(2m+2n)$-fold sum for $\omega_b$ in terms of $4mn$-fold integrals The asymptotics of the $T^{(n)}$'s and ${T'}^{(n)}$'s Replacement of the $T^{(k)}$'s and ${T'}^{(k)}$'s by their asymptotics Proof of Proposition 7.2 The asymptotics of a multidimensional Laplace integral The asymptotics of $\omega_b$. Proof of Theorem 2.2 Another simple product formula for correlations along the boundary The asymptotics of $\bar{\omega}_b$. Proof of Theorem 2.1 A conjectured general two dimensional Superposition Principle Three dimensions and concluding remarks Bibliography Part B. Plane Partitions I: A Generalization of MacMahon's Formula: Introduction Two families of regions Reduction to simply-connected regions Recurrences for $\textup{M}(R_{{\bf l},{\bf q}}(x))$ and $\textup{M}(\bar{R}_{{\bf l},{\bf q}}(x))$ Proof of Proposition 2.1 The guessing of $\textup{M}(R_{{\bf l},{\bf q}}(x))$ and $\textup{M}(\bar{R}_{{\bf l},{\bf q}}(x))$ Bibliography |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2005050800 |
| ISBN | 9780821837948 |
| ISBN | 082183794X (Trade Paper) Active Record |
| Standard identifier# | 9780821837948 |
| Stock number | MEMO/178/839 00001436 |