Contents
Abstract ix
Part A.
A Random Tiling Model for Two Dimensional Electrostatics 1
1. Introduction 3
2. Definitions, statement of results and physical interpretation 6
3. Reduction to boundary-influenced correlations 16
4. A simple product formula for correlations along the boundary 18
5. A (2m -f 2n)-fold sum for Ub 25
6. Separation of the (2ra+2n)-fold sum for UJ^ in terms of 4ran-fold integrals 37
7. The asymptotics of the T^'s and T'(n)'s 42
8. Replacement of the T^k^s and T^ ^'s by their asymptotics 52
9. Proof of Proposition 7.2 56
10. The asymptotics of a multidimensional Laplace integral 65
11. The asymptotics of UJ^. Proof of Theorem 2.2 69
12. Another simple product formula for correlations along the boundary 80
13. The asymptotics of £&. Proof of Theorem 2.1 84
14. A conjectured general two dimensional Superposition Principle 94
15. Three dimensions and concluding remarks 99
Bibliography 104
Part B.
Plane Partitions I: A Generalization of MacMahon's Formula 107
1. Introduction 109
2. Two families of regions 116
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