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Subshifts of finite type which have completely positive entropy
1. | Department of Mathematics, University of Washington, Seattle, WA 98195-4350, United States |
References:
[1] |
R. Berger, The undecidability of the domino problem, Memoirs Amer. Math. Soc., 66 (1966). |
[2] |
H. W. J. Blöte and H. J. Hilhorst, Roughening transitions and the zero-temperature triangular Ising antiferromagnet, J. Phys. A, 15 (1982), L631.
doi: 10.1088/0305-4470/15/11/011. |
[3] |
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.
doi: 10.1214/aop/1176989121. |
[4] |
R. Burton and J. E. Steif, Non-uniqueness of measures of maximal entropy for subshifts of finite type, Ergodic Theory Dynam. Systems, 14 (1994), 213-235.
doi: 10.1017/S0143385700007859. |
[5] |
H. Cohn, R. Kenyon and J. Propp, A variational principle for domino tilings, Journal Of The AMS, 14 (2001), 297-346. |
[6] |
J. P. Conze, Entropie d'un groupe abélian de transformations1. Z Wasrscheinlichkeitstheorie Verw. Geiete, 25 (1972), 11-30. |
[7] |
J. Feldman, New $K$-automorphisms and a problem of Kakutani, Israel J. Math., 24 (1976), 16-38.
doi: 10.1007/BF02761426. |
[8] |
N. A. Friedman and D. Ornstein, On isomorphism of weak Bernoulli transformations, Advances in Math., 5 (1970), 365-394.
doi: 10.1016/0001-8708(70)90010-1. |
[9] |
C. Hoffman, A Markov random field which is $K$ but not Bernoulli, Israel J. Math., 112 (1999), 249-269.
doi: 10.1007/BF02773484. |
[10] |
F. den Hollander and J. Steif, On K-automorphisms, Bernoulli shifts and Markov random fields, Ergodic Theory and Dynamical Systems, to appear. |
[11] |
R. Kenyon, The Laplacian and Dirac operators on critical planar graphs, Invent. Math., 150 (2002), 409-439.
doi: 10.1007/s00222-002-0249-4. |
[12] |
R. Kenyon, Conformal invariance of domino tiling, Ann. Probab., 28 (2000), 759-795.
doi: 10.1214/aop/1019160260. |
[13] |
R. Kenyon, Local statistics of lattice dimers, Ann. Inst. H. Poincaré, Probabilités, 33 (1997), 591-618. |
[14] |
R. Kenyon, Dominos and the Gaussian free field, Ann. Probab., 29 (2001), 1128-1137.
doi: 10.1214/aop/1015345599. |
[15] |
R. Kenyon, A. Okounkov and S. Sheffield, Dimers and amoebae, Ann. of Math. (2), 163 (2006), 1019-1056.
doi: 10.4007/annals.2006.163.1019. |
[16] |
F. Ledrappier, Un champ markovien peut être d'entropie nulle et mélangeant, C. R. Acad. Sci. Paris Sér. A-B, 287 (1978), A561-A563. |
[17] |
D. Lind, B. Marcus, "An Introduction to Symbolic Dynamics and Coding," Cambridge University Press, Cambridge, 1995. |
[18] |
I. Meilijson, Mixing properties of a class of skew-products, Israel J. Math., 19 (1974), 266-270.
doi: 10.1007/BF02757724. |
[19] |
S. Sheffield, Uniqueness of maximal entropy measure on essential spanning forests, Ann. Probab., 34 (2006), 857-864.
doi: 10.1214/009117905000000765. |
[20] |
W. P. Thurston, Conway's tiling groups, Amer. Math. Monthly, 97 (1990), 757-773.
doi: 10.2307/2324578. |
show all references
References:
[1] |
R. Berger, The undecidability of the domino problem, Memoirs Amer. Math. Soc., 66 (1966). |
[2] |
H. W. J. Blöte and H. J. Hilhorst, Roughening transitions and the zero-temperature triangular Ising antiferromagnet, J. Phys. A, 15 (1982), L631.
doi: 10.1088/0305-4470/15/11/011. |
[3] |
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.
doi: 10.1214/aop/1176989121. |
[4] |
R. Burton and J. E. Steif, Non-uniqueness of measures of maximal entropy for subshifts of finite type, Ergodic Theory Dynam. Systems, 14 (1994), 213-235.
doi: 10.1017/S0143385700007859. |
[5] |
H. Cohn, R. Kenyon and J. Propp, A variational principle for domino tilings, Journal Of The AMS, 14 (2001), 297-346. |
[6] |
J. P. Conze, Entropie d'un groupe abélian de transformations1. Z Wasrscheinlichkeitstheorie Verw. Geiete, 25 (1972), 11-30. |
[7] |
J. Feldman, New $K$-automorphisms and a problem of Kakutani, Israel J. Math., 24 (1976), 16-38.
doi: 10.1007/BF02761426. |
[8] |
N. A. Friedman and D. Ornstein, On isomorphism of weak Bernoulli transformations, Advances in Math., 5 (1970), 365-394.
doi: 10.1016/0001-8708(70)90010-1. |
[9] |
C. Hoffman, A Markov random field which is $K$ but not Bernoulli, Israel J. Math., 112 (1999), 249-269.
doi: 10.1007/BF02773484. |
[10] |
F. den Hollander and J. Steif, On K-automorphisms, Bernoulli shifts and Markov random fields, Ergodic Theory and Dynamical Systems, to appear. |
[11] |
R. Kenyon, The Laplacian and Dirac operators on critical planar graphs, Invent. Math., 150 (2002), 409-439.
doi: 10.1007/s00222-002-0249-4. |
[12] |
R. Kenyon, Conformal invariance of domino tiling, Ann. Probab., 28 (2000), 759-795.
doi: 10.1214/aop/1019160260. |
[13] |
R. Kenyon, Local statistics of lattice dimers, Ann. Inst. H. Poincaré, Probabilités, 33 (1997), 591-618. |
[14] |
R. Kenyon, Dominos and the Gaussian free field, Ann. Probab., 29 (2001), 1128-1137.
doi: 10.1214/aop/1015345599. |
[15] |
R. Kenyon, A. Okounkov and S. Sheffield, Dimers and amoebae, Ann. of Math. (2), 163 (2006), 1019-1056.
doi: 10.4007/annals.2006.163.1019. |
[16] |
F. Ledrappier, Un champ markovien peut être d'entropie nulle et mélangeant, C. R. Acad. Sci. Paris Sér. A-B, 287 (1978), A561-A563. |
[17] |
D. Lind, B. Marcus, "An Introduction to Symbolic Dynamics and Coding," Cambridge University Press, Cambridge, 1995. |
[18] |
I. Meilijson, Mixing properties of a class of skew-products, Israel J. Math., 19 (1974), 266-270.
doi: 10.1007/BF02757724. |
[19] |
S. Sheffield, Uniqueness of maximal entropy measure on essential spanning forests, Ann. Probab., 34 (2006), 857-864.
doi: 10.1214/009117905000000765. |
[20] |
W. P. Thurston, Conway's tiling groups, Amer. Math. Monthly, 97 (1990), 757-773.
doi: 10.2307/2324578. |
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