Local statistics of lattice dimers

Richard Kenyon

Annales de l'I.H.P. Probabilités et statistiques (1997)

  • Volume: 33, Issue: 5, page 591-618
  • ISSN: 0246-0203

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Kenyon, Richard. "Local statistics of lattice dimers." Annales de l'I.H.P. Probabilités et statistiques 33.5 (1997): 591-618. <http://eudml.org/doc/77583>.

@article{Kenyon1997,
author = {Kenyon, Richard},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {dimers; dominos; measure of maximal entropy},
language = {eng},
number = {5},
pages = {591-618},
publisher = {Gauthier-Villars},
title = {Local statistics of lattice dimers},
url = {http://eudml.org/doc/77583},
volume = {33},
year = {1997},
}

TY - JOUR
AU - Kenyon, Richard
TI - Local statistics of lattice dimers
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1997
PB - Gauthier-Villars
VL - 33
IS - 5
SP - 591
EP - 618
LA - eng
KW - dimers; dominos; measure of maximal entropy
UR - http://eudml.org/doc/77583
ER -

References

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  2. [BP] R. Burton and R. Pemantle, Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transfer impedances, Ann. Probab., Vol. 21, 1993, pp. 1329-1371. Zbl0785.60007MR1235419
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  4. [CEP] H. Cohn and N. Elkies, J. Propp, Local statistics for random domino tilings of the Aztec diamond, Duke Math. J., Vol. 85, 1996, pp. 117-166. Zbl0866.60018MR1412441
  5. [CKP] H. Cohn and R. Kenyon, J. Propp, in preparation. 
  6. [EKLP] N. Elkies, G. Kuperberg and M. Larsen, J. Propp, Alternating sign matrices and domino tilings. J. Alg. Combinatorics, Vol. 1, 1992, pp. 111-132. Zbl0779.05009MR1226347
  7. [FS] M.E. Fisher and J. Stephenson, Statistical mechanics of dimers on a plane lattice II. Dimer correlations and monomers, Phys. Rev. , Vol. 132, 1963, pp. 1411-1431. Zbl0132.22304MR158705
  8. [HG] C.A. Hurst and H.S. Green, New solution of the Ising problem for a rectangular lattice, J. Chem. Phys., Vol. 33, 1960, pp. 1059-1062. MR116546
  9. [K1] P.W. Kasteleyn, The statistics of dimers on a lattice, Physica, Vol. 27, 1961, pp. 1209-1225. Zbl1244.82014
  10. [K2] P.W. Kasteleyn, Graph theory and crystal physics, in Graph Theory and Theoretical Physics, Academic Press, London1967. Zbl0205.28402MR253689
  11. [MPW] E.W. Montroll, R.B. Potts and J.C. Ward, Correlations and spontaneous magnetization of the two-dimensional Ising model, J. Math. Phys., Vol. 4, 1963, p. 308-322. MR148406
  12. [P] K. Petersen, Ergodic theory, Cambridge studes in advanced mathematics 2, Cambridge university press, Cambridge, 1983. Zbl0507.28010MR833286
  13. [PW] J. Propp and D. Wilson, in preparation. 
  14. [St] J. Stephenson, Ising-model spin correlations on the triangular lattice, J. Math. Phys., Vol. 5, 1964, pp. 1009-1024. MR168310
  15. [T] W. Thurston , Conway's tiling groups, Am. Math. Monthly, Vol. 97, 1990, pp. 757-773. Zbl0714.52007MR1072815
  16. [TF] H. Templerley and M. Fisher, The dimer problem in statistical mechanics - an exact result. Phil Mag., Vol. 6, 1961, pp. 1061-1063. Zbl0126.25102MR136398
  17. [W] T. Wu, Dimers on rectangular lattices, J. Math. Phys, Vol. 3, 1962, pp. 1265-1266. Zbl0113.23406MR149896

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