Duke Mathematical Journal

Local statistics for random domino tilings of the Aztec diamond

Henry Cohn, Noam Elkies, and James Propp

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J. Volume 85, Number 1 (1996), 117-166.

Dates
First available in Project Euclid: 19 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077243040

Mathematical Reviews number (MathSciNet)
MR1412441

Zentralblatt MATH identifier
0866.60018

Digital Object Identifier
doi:10.1215/S0012-7094-96-08506-3

Subjects
Primary: 52C20: Tilings in $2$ dimensions [See also 05B45, 51M20]
Secondary: 11L07: Estimates on exponential sums 82B26: Phase transitions (general)

Citation

Cohn, Henry; Elkies, Noam; Propp, James. Local statistics for random domino tilings of the Aztec diamond. Duke Math. J. 85 (1996), no. 1, 117--166. doi:10.1215/S0012-7094-96-08506-3. http://projecteuclid.org/euclid.dmj/1077243040.


Export citation

References

  • [AS] N. Alon and J. Spencer, The probabilistic method, Wiley-Interscience Series in Discrete Mathematics and Optimization, John Wiley & Sons Inc., New York, 1992.
  • [vB] H. van Beijeren, Exactly solvable model for the roughening transition of a crystal surface, Phys. Rev. Lett. 38 (1977), 993–996.
  • [BH] H. W. J. Blöte and H. J. Hilhorst, Roughening transitions and the zero-temperature triangular Ising antiferromagnet, J. Phys. A 15 (1982), no. 11, L631–L637.
  • [dB] N. G. de Bruijn, Asymptotic methods in analysis, Dover Publications Inc., New York, 1981.
  • [BP] R. Burton and R. Pemantle, Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transfer-impedances, Ann. Probab. 21 (1993), no. 3, 1329–1371.
  • [D] R. Durrett, Probability, The Wadsworth & Brooks/Cole Statistics/Probability Series, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1991.
  • [EKLP]1 N. Elkies, G. Kuperberg, M. Larsen, and J. Propp, Alternating-sign matrices and domino tilings. I, J. Algebraic Combin. 1 (1992), no. 2, 111–132.
  • [EKLP]2 N. Elkies, G. Kuperberg, M. Larsen, and J. Propp, Alternating-sign matrices and domino tilings. II, J. Algebraic Combin. 1 (1992), no. 3, 219–234.
  • [E] V. Elser, Solution of the dimer problem on a hexagonal lattice with boundary, J. Phys. A 17 (1984), no. 7, 1509–1513.
  • [G] H.-O. Georgii, Gibbs measures and phase transitions, de Gruyter Studies in Mathematics, vol. 9, Walter de Gruyter & Co., Berlin, 1988.
  • [GIP] I. Gessel, A. Ionescu, and J. Propp, Counting constrained domino tilings of Aztec diamonds, preprint, 1996.
  • [GK] S. W. Graham and G. Kolesnik, van der Corput's method of exponential sums, London Mathematical Society Lecture Note Series, vol. 126, Cambridge University Press, Cambridge, 1991.
  • [GG] D. Grensing and G. Grensing, Boundary effects in the dimer problem on a non-Bravais lattice, J. Math. Phys. 24 (1983), no. 3, 620–630.
  • [JPS] W. Jockusch, J. Propp, and P. Shor, Random domino tilings and the arctic circle theorem, preprint, 1995.
  • [Ka] 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.
  • [Kr] U. Krengel, Ergodic theorems, de Gruyter Studies in Mathematics, vol. 6, Walter de Gruyter & Co., Berlin, 1985.
  • [L] L. S. Levitov, Equivalence of the dimer resonating-valence-bond problem to the quantum roughening problem, Phys. Rev. Lett. 64 (1990), no. 1, 92–94.
  • [MS] F. J. MacWilliams and N. J. A. Sloane, The theory of error-correcting codes. I, North-Holland Publishing Co., Amsterdam, 1977.
  • [NHB] B. Nienhuis, H. J. Hilhorst, and H. W. J. Blöte, Triangular SOS models and cubic-crystal shapes, J. Phys. A 17 (1984), no. 18, 3559–3581.
  • [PW] J. G. Propp and D. B. Wilson, Exact sampling with coupled Markov chains and applications to statistical mechanics, to appear in Random Structures Algorithms.
  • [R] J. Rauch, Partial differential equations, Graduate Texts in Mathematics, vol. 128, Springer-Verlag, New York, 1991.
  • [SZ] H. Sachs and H. Zernitz, Remark on the dimer problem, Discrete Appl. Math. 51 (1994), no. 1-2, 171–179.
  • [STCR] N. Saldanha, C. Tomei, M. Casarin, Jr., and D. Romualdo, Spaces of domino tilings, Discrete Comput. Geom. 14 (1995), no. 2, 207–233.
  • [T] W. P. Thurston, Conway's tiling groups, Amer. Math. Monthly 97 (1990), no. 8, 757–773.