Local statistics for random domino tilings of the Aztec diamond

Duke Mathematical Journal

Volumn 85, Issue 1, 1996, Pages 117-166

  Cohn, Henry ^a   Elkies, Noam ^a   Propp, James ^b  

^a HARVARD UNIVERSITY   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001937215     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-96-08506-3     Document Type: Article

References (23)

1. N. ALON AND J. SPENCER, The Probabilistic Method, Wiley, New York, 1992.
2. H. VAN BEIJEREN, Exactly solvable model for the roughening transition of a crystal surface, Phys. Rev. Lett. 38 (1977), 993-996.
3. H. W. J. BLÖTE AND H. J. HILHORST, Roughening transitions and the zero-temperature triangular Ising antiferromagnet, J. Phys. A 15 (1982), L631-L637.
4. N. G. DE BRUUN, Asymptotic Methods in Analysis, Dover Publications, Inc., New York, 1981.
5. R. BURTON AND R. PEMANTLE, Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transfer-impedances, Ann. Probab. 21 (1993), 1329-1371.
6. R. DURRETT, Probability: Theory and Examples, Wadsworth and Brooks/Cole Pacific Grove, Calif., 1991.
7. N. ELKIES, G. KUPERBERG, M. LARSEN, AND J. PROPP, Alternating sign matrices and domino tilings, J. Algebraic Combin. 1 (1992), 111-132 and 219-234.
8. V. ELSER, Solution of the dimer problem on a hexagonal lattice with boundary, J. Phys. A 17 (1984), 1509-1513.
9. H.-O. GEORGII, Gibbs Measures and Phase Transitions, De Gruyter, New York, 1988.
10. I. GESSEL, A. IONESCU, AND J. PROPP, Counting constrained domino tilings of Aztec diamonds, preprint, 1996.
11. S. W. GRAHAM AND G. KOLESNIK, Van der Corput's Method of Exponential Sums, Cambridge University Press, Cambridge, 1991.
12. D. GRENSING AND G. GRENSING, Boundary effects in the dimer problem on a non-Bravais lattice, J. Math. Phys. 24 (1983), 620-630.
13. W. JOCKUSCH, J. PROPP, AND P. SHOR, Random domino tilings and the arctic circle theorem, preprint, 1995.
14. P. W. KASTELEYN, The statistics of dimers on a lattice, I. The number of dimer arrangements on a quadratic lattice, Physica 27 (1961), 1209-1225.
15. U. KRENGEL, Ergodic Theorems, W. de Gruyter, New York, 1985.
16. L. S. LEVITOV, Equivalence of the dimer resonating-valence-bond problem to the quantum roughening problem, Phys. Rev. Lett. 64 (1990), 92-94.
17. F. J. MACWILLIAMS AND N. J. A. SLOANE, The Theory of Error-Correcting Codes, North-Holland Publishing Company, Amsterdam, 1978.
18. B. NIENHUIS, H. J. HILHORST, AND H. W. J. BLÖTE, Triangular SOS models and cubic-crystal shapes, J. Phys. A 17 (1984), 3559-3581.
19. J. G. PROPP AND D. B. WILSON, Exact sampling with coupled Markov chains and applications to statistical mechanics, to appear in Random Structures Algorithms.
20. J. RAUCH, Partial Differential Equations, Springer-Verlag, New York, 1991.
21. H. SACHS AND H. ZERNITZ, Remark on the dimer problem, Discrete Appl. Math. 51 (1994), 171-179.
22. N. SALDANHA, C. TOMEI, M. CASARIN JR., AND D. ROMUALDO, Spaces of domino tilings, Discrete Comput. Geom. 14 (1995), 207-233.
23. W. P. THURSTON, Conway's tilinq groups, Amer. Math. Monthly 97 (1990), 757-773.