Planar dimers and Harnack curves

Duke Mathematical Journal

Volumn 131, Issue 3, 2006, Pages 499-524

  Kenyon, Richard ^a   Okounkov, Andrei ^b  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33644810420     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-06-13134-4     Document Type: Article

References (21)

1. E. ARBARELLO, M. CORNALBA, P. A. GRIFFITHS, and J. HARRIS, Geometry of Algebraic Curves, Vol. I, Grundlehren Math. Wiss. 267, Springer, New York, 1985. MR 0770932
2. V. I. ARNOLD and S. P. NOVIKOV, eds., Dynamical Systems, VII, Encyclopaedia Math. Sci. 16, Springer, Berlin, 1994. MR 1256257
3. O. BABELON, D. BERNARD, and M. TALON, Introduction to Classical Integrable Systems, Cambridge Monogr. Math. Phys., Cambridge Univ. Press, Cambridge, 2003. MR 1995460
4. A. BEAUVILLE, "Systèmes hamiltoniens complètement intégrables associés aux surfaces K 3" in Problems in the Theory of Surfaces and Their Classification (Cortona, Italy, 1988), Sympos. Math. 32, Academic Press, London, 1991, 25-31. MR 1273370
5. _, Determinantal hypersurfaces, Michigan Math. J. 48 (2000), 39-64. MR 1786479
6. R. J. COOK and A. D. THOMAS, Line bundles and homogeneous matrices, Quart. J. Math. Oxford Ser. (2) 30 (1979), 423-429. MR 0559048
7. I. A. DYNNIKOV and S. P. NOVIKOV, Discrete spectral symmetries of small-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds, Russian Math. Surveys 52 (1997), 1057-1116. MR 1490030
8. _, Geometry of the triangle equation on two-manifolds, Mosc. Math. J. 3 (2003), 419-438. MR 2025267
9. D. GIESEKER, H. KNÖRRER, and E. TRUBOWITZ, The Geometry of Algebraic Fermi Curves, Perspect. Math. 14, Academic Press, Boston, 1993. MR 1184395
10. A. GORSKY, N. NEKRASOV, and V. RUBTSOV, Hilbert schemes, separated variables, and D-branes, Comm. Math. Phys. 222 (2001), 299-318. MR 1859601
11. J. C. HURTUBISE, Integrable systems and algebraic surfaces, Duke Math. J. 83 (1996), 19-50. MR 1388842
12. P. KASTELEYN, Statistics of dimers on a lattice, Physica 27 (1961), 1209-1225.
13. R. KENYON, The Laplacian and Dirac operators on critical planar graphs, Invent. Math. 150 (2002), 409-439. MR 1933589
14. _, An introduction to the dimer model, ICTP Lecture Notes Ser. 17 (2004), http://users.ictp.it/~pub-off/lectures/vol17.html
15. R. KENYON, A. OKOUNKOV, and S. SHEFFIELD, Dimers and amoebae, to appear in Ann. of Math. (2), preprint, arXiv:math-ph/0311005
16. G. MIKHALKIN, Real algebraic curves, the moment map and amoebas, Ann. of Math. (2) 151 (2000), 309-326. MR 1745011
17. G. MIKHALKIN and H. RULLGÅRD, Amoebas of maximal area, Internat. Math. Res. Notices 2001, no. 9, 441-451. MR 1829380
18. A. A. OBLOMKOV, Difference operators on two-dimensional regular lattices, Theoret. and Math. Phys. 127 (2001), 435-445. MR 1863517
19. J. PROPP, Generalized domino-shuffling, Theoret. Comput. Sci. 303 (2003), 267-301. MR 1990768
20. E. K. SKLYANIN, "Separation of variables - new trends" in Quantum Field Theory, Integrable Models and Beyond (Kyoto, 1994), Progr. Theoret. Phys. Suppl. 118 (1995), 35-60. MR 1356514
21. V. VINNIKOV, Selfadjoint determinantal representations of real plane curves, Math. Ann. 296 (1993), 453-479. MR 1225986