TY  - BOOK
AU  - Ciucu,Mihai
TI  - A random tiling model for two dimensional electrostatics
T2  - Memoirs of the American Mathematical Society, 
SN  - 9781470404406 (online)
AV  - QA3QA166.8 .A57 no. 839
U1  - 510 s537/.2 22
PY  - 2005///
CY  - Providence, R.I.
PB  - American Mathematical Society
KW  - Tiling (Mathematics)
KW  - Electrostatics
KW  - Statistical mechanics
N1  - "Volume 178, number 839 (third of 5 numbers)."; Includes bibliographical references (p. 144); 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 $\mathrm {M}(\bar {R}_{\mathbf {l}, \mathbf {q}}(x))$; Access is restricted to licensed institutions; Electronic reproduction; Providence, Rhode Island; American Mathematical Society; 2012
UR  - http://www.ams.org/memo/0839
UR  - http://dx.doi.org/10.1090/memo/0839
ER  -