Ciucu, Mihai, 1968-
A random tiling model for two dimensional electrostatics / [electronic resource] Mihai Ciucu. - Providence, R.I. : American Mathematical Society, 2005. - 1 online resource (ix, 144 p. : ill.) - Memoirs of the American Mathematical Society, v. 839 0065-9266 (print); 1947-6221 (online); .
"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 $T^$'s and $T'^$'s 8. Replacement of the $T^$'s and $T'^$'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 $\bar _b$. 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 $\mathrm (R_, \mathbf }(x))$ and $\mathrm (\bar _, \mathbf }(x))$ 5. Proof of Proposition 2.1 6. The guessing of $\mathrm (R_, \mathbf }(x))$ and $\mathrm (\bar _, \mathbf }(x))$
Access is restricted to licensed institutions
Electronic reproduction.
Providence, Rhode Island :
American Mathematical Society.
2012
Mode of access : World Wide Web
9781470404406 (online)
Tiling (Mathematics)
Electrostatics.
Statistical mechanics.
QA3 QA166.8 / .A57 no. 839
510 s 537/.2
A random tiling model for two dimensional electrostatics / [electronic resource] Mihai Ciucu. - Providence, R.I. : American Mathematical Society, 2005. - 1 online resource (ix, 144 p. : ill.) - Memoirs of the American Mathematical Society, v. 839 0065-9266 (print); 1947-6221 (online); .
"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 $T^$'s and $T'^$'s 8. Replacement of the $T^$'s and $T'^$'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 $\bar _b$. 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 $\mathrm (R_, \mathbf }(x))$ and $\mathrm (\bar _, \mathbf }(x))$ 5. Proof of Proposition 2.1 6. The guessing of $\mathrm (R_, \mathbf }(x))$ and $\mathrm (\bar _, \mathbf }(x))$
Access is restricted to licensed institutions
Electronic reproduction.
Providence, Rhode Island :
American Mathematical Society.
2012
Mode of access : World Wide Web
9781470404406 (online)
Tiling (Mathematics)
Electrostatics.
Statistical mechanics.
QA3 QA166.8 / .A57 no. 839
510 s 537/.2