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Volumn 246, Issue 2, 2004, Pages 311-332

A Particular Bit of Universality: Scaling Limits of Some Dependent Percolation Models

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EID: 2142651448     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-004-1042-6     Document Type: Article
Times cited : (10)

References (52)
  • 1
    • 0007122530 scopus 로고
    • The geometry of critical percolation and conformal invariance
    • H. Balin, ed., Singapore: World Scientific
    • Aizenman, M.: The geometry of critical percolation and conformal invariance. In Stat. Phys. 19, H. Balin, ed., Singapore: World Scientific, 1995
    • (1995) Stat. Phys. , vol.19
    • Aizenman, M.1
  • 2
    • 0039094784 scopus 로고    scopus 로고
    • Scaling limit for the incipient spanning clusters
    • K. Golden, G. Grimmett, R. James, G. Milton, P. Sen, eds., Berlin-Heidelberg-New York: Springer
    • Aizenman, M.: Scaling limit for the incipient spanning clusters. In: Mathematics of Multiscale Materials; the IMA Volumes in Mathematics and its Applications, K. Golden, G. Grimmett, R. James, G. Milton, P. Sen, eds., Berlin-Heidelberg-New York: Springer, 1998
    • (1998) Mathematics of Multiscale Materials; the IMA Volumes in Mathematics and Its Applications
    • Aizenman, M.1
  • 3
    • 0001056718 scopus 로고    scopus 로고
    • Holder regularity and dimension bounds for random curves
    • Aizenman, M., Burchard, A.: Holder regularity and dimension bounds for random curves. Duke Math. J. 99, 419-453 (1999)
    • (1999) Duke Math. J. , vol.99 , pp. 419-453
    • Aizenman, M.1    Burchard, A.2
  • 4
    • 0033415760 scopus 로고    scopus 로고
    • Scaling Limits for Minimal and Random Spanning Trees in Two Dimensions
    • Aizenman, M., Burchard, A., Newman, C.M., Wilson, D.B.: Scaling Limits for Minimal and Random Spanning Trees in Two Dimensions. Random Struct. Alg. 15, 319-367 (1999)
    • (1999) Random Struct. Alg. , vol.15 , pp. 319-367
    • Aizenman, M.1    Burchard, A.2    Newman, C.M.3    Wilson, D.B.4
  • 5
    • 0004542587 scopus 로고
    • Infinite conformal symmetry of critical fluctuations in two dimensions
    • Belavin, A.A., Polyakov, A.M., Zamolodchikov, A.B.: Infinite conformal symmetry of critical fluctuations in two dimensions. J. Stat. Phys. 34, 763-774 (1984)
    • (1984) J. Stat. Phys. , vol.34 , pp. 763-774
    • Belavin, A.A.1    Polyakov, A.M.2    Zamolodchikov, A.B.3
  • 6
    • 0010882054 scopus 로고
    • Infinite conformal symmetry in two-dimensional quantum field theory
    • Belavin, A.A., Polyakov, A.M., Zamolodchikov, A.B.: Infinite conformal symmetry in two-dimensional quantum field theory. Nucl. Phys. B241, 333-380 (1984)
    • (1984) Nucl. Phys. , vol.B241 , pp. 333-380
    • Belavin, A.A.1    Polyakov, A.M.2    Zamolodchikov, A.B.3
  • 10
    • 0036339031 scopus 로고    scopus 로고
    • Clusters and recurrence in the two-dimensional zero-temperature stochastic Ising model
    • Camia, F., De Santis, E., Newman, C. M.: Clusters and recurrence in the two-dimensional zero-temperature stochastic Ising model. Ann. Appl. Probab. 12, 565-580 (2002)
    • (2002) Ann. Appl. Probab. , vol.12 , pp. 565-580
    • Camia, F.1    De Santis, E.2    Newman, C.M.3
  • 11
    • 85088006223 scopus 로고    scopus 로고
    • The Percolation Transition in the Zero-Temperature Domany Model
    • to appear
    • Camia, F., Newman, C.M.: The Percolation Transition in the Zero-Temperature Domany Model. J. Stat. Phys., to appear
    • J. Stat. Phys.
    • Camia, F.1    Newman, C.M.2
  • 12
    • 4344576881 scopus 로고    scopus 로고
    • Continuum Nonsimple Loops and 2D Critical Percolation
    • to appear
    • Camia, F., Newman, C.M.: Continuum Nonsimple Loops and 2D Critical Percolation. J. Stat. Phys., to appear
    • J. Stat. Phys.
    • Camia, F.1    Newman, C.M.2
  • 13
    • 2142834296 scopus 로고    scopus 로고
    • Camia, F., Newman, C.M.: In preparation
    • Camia, F., Newman, C.M.: In preparation
  • 14
    • 0345973287 scopus 로고    scopus 로고
    • Approach to fixation for zero-temperature stochastic Ising models on the hexagonal lattice
    • V. Sidoravicius, ed., Progress in Probability, Basel-Boston: Birkhäuser
    • Camia, F., Newman, C.M., Sidoravicius, V.: Approach to fixation for zero-temperature stochastic Ising models on the hexagonal lattice. In: In and out of equilibrium: Probability with a Physics Flavor V. Sidoravicius, ed., Progress in Probability 51, Basel-Boston: Birkhäuser, 2002, pp. 163-183
    • (2002) In and Out of Equilibrium: Probability with a Physics Flavor , vol.51 , pp. 163-183
    • Camia, F.1    Newman, C.M.2    Sidoravicius, V.3
  • 16
    • 0000898051 scopus 로고
    • Critical percolation in finite geometries
    • Cardy, J.L.: Critical percolation in finite geometries. J. Phys. A 25, L201-L206 (1992)
    • (1992) J. Phys. A , vol.25
    • Cardy, J.L.1
  • 18
    • 0013387184 scopus 로고
    • Exact results for two- and three-dimensional Ising and Potts models
    • Domany, E.: Exact results for two- and three-dimensional Ising and Potts models. Phys. Rev. Lett. 52, 871-874 (1984)
    • (1984) Phys. Rev. Lett. , vol.52 , pp. 871-874
    • Domany, E.1
  • 20
    • 0036022801 scopus 로고    scopus 로고
    • Stretched exponential fixation in stochastic Ising models at zero temperature
    • Fontes, L.R., Schonmann, R.H., Sidoravicius, V.: Stretched exponential fixation in stochastic Ising models at zero temperature. Commun. Math. Phys. 228, 495-518 (2002)
    • (2002) Commun. Math. Phys. , vol.228 , pp. 495-518
    • Fontes, L.R.1    Schonmann, R.H.2    Sidoravicius, V.3
  • 21
    • 0000412970 scopus 로고
    • On the uniqueness of the infinite occupied cluster in dependent two-dimensional site percolation
    • Gandolfi, A., Keane, M., Russo, L.: On the uniqueness of the infinite occupied cluster in dependent two-dimensional site percolation. Ann. Probab. 16, 1147-1157 (1988)
    • (1988) Ann. Probab. , vol.16 , pp. 1147-1157
    • Gandolfi, A.1    Keane, M.2    Russo, L.3
  • 22
    • 0034348255 scopus 로고    scopus 로고
    • Zero-temperature dynamics of ±J spin glasses and related models
    • Gandolfi, A., Newman, C.M., Stein, D.L.: Zero-temperature dynamics of ±J spin glasses and related models. Commun. Math. Phys. 214, 373-387 (2000)
    • (2000) Commun. Math. Phys. , vol.214 , pp. 373-387
    • Gandolfi, A.1    Newman, C.M.2    Stein, D.L.3
  • 24
    • 36849127979 scopus 로고
    • The Principle of Corresponding States
    • Guggenheim, E.A.: The Principle of Corresponding States. J. Chem. Phys. 13, 253-261 (1945)
    • (1945) J. Chem. Phys. , vol.13 , pp. 253-261
    • Guggenheim, E.A.1
  • 25
    • 0001041882 scopus 로고
    • A correlation inequality for Markov processes in partially ordered state spaces
    • Harris, T.E.: A correlation inequality for Markov processes in partially ordered state spaces. Ann. Probab. 5, 451-454 (1977)
    • (1977) Ann. Probab. , vol.5 , pp. 451-454
    • Harris, T.E.1
  • 26
    • 0034337830 scopus 로고    scopus 로고
    • Zero-temperature Ising spin dynamics on the homogeneous tree of degree three
    • Howard, C.D.: Zero-temperature Ising spin dynamics on the homogeneous tree of degree three. J. Appl. Probab. 37, 736-747 (2000)
    • (2000) J. Appl. Probab. , vol.37 , pp. 736-747
    • Howard, C.D.1
  • 27
    • 0346492931 scopus 로고    scopus 로고
    • The percolation transition for the zero-temperature stochastic Ising model on the hexagonal lattice
    • Howard, C.D., Newman, C.M.: The percolation transition for the zero-temperature stochastic Ising model on the hexagonal lattice. J. Stat. Phys. 111, 57-72 (2003)
    • (2003) J. Stat. Phys. , vol.111 , pp. 57-72
    • Howard, C.D.1    Newman, C.M.2
  • 28
    • 0012566413 scopus 로고    scopus 로고
    • Values of Brownian intersection exponents I: Half-plane exponents
    • Lawler, G., Schramm, O., Werner, W.: Values of Brownian intersection exponents I: Half-plane exponents. Acta Math. 187, 237-273 (2001)
    • (2001) Acta Math. , vol.187 , pp. 237-273
    • Lawler, G.1    Schramm, O.2    Werner, W.3
  • 29
    • 0000467140 scopus 로고    scopus 로고
    • Values of Brownian intersection exponents II: Plane exponents
    • Lawler, G., Schramm, O., Werner, W.: Values of Brownian intersection exponents II: Plane exponents. Acta Math. 187, 275-308 (2001)
    • (2001) Acta Math. , vol.187 , pp. 275-308
    • Lawler, G.1    Schramm, O.2    Werner, W.3
  • 30
    • 1342292650 scopus 로고    scopus 로고
    • Values of Brownian intersection exponents III: Two-sided exponents
    • Lawler, G., Schramm, O., Werner, W.: Values of Brownian intersection exponents III: Two-sided exponents. Ann. Inst. Henri Poincaré 38, 109-123 (2002)
    • (2002) Ann. Inst. Henri Poincaré , vol.38 , pp. 109-123
    • Lawler, G.1    Schramm, O.2    Werner, W.3
  • 31
    • 0036948020 scopus 로고    scopus 로고
    • Analyticity of intersection exponents for planar Brownian motion
    • Lawler, G., Schramm, O., Werner, W.: Analyticity of intersection exponents for planar Brownian motion. Acta Math. 189, 179-201 (2002)
    • (2002) Acta Math. , vol.189 , pp. 179-201
    • Lawler, G.1    Schramm, O.2    Werner, W.3
  • 33
    • 0345371457 scopus 로고    scopus 로고
    • Conformal invariance of planar loop-erased random walk and uniform spanning trees
    • to appear. Preprint arXiv:math.PR/0112234
    • Lawler, G., Schramm, O., Werner, W.: Conformal invariance of planar loop-erased random walk and uniform spanning trees. Ann. Probab., to appear. Preprint arXiv:math.PR/0112234 (2003)
    • (2003) Ann. Probab.
    • Lawler, G.1    Schramm, O.2    Werner, W.3
  • 34
    • 0141680586 scopus 로고    scopus 로고
    • Conformal restriction: The chordal case
    • Lawler, G., Schramm, O., Werner, W.: Conformal restriction: The chordal case. J. Amer Math. Soc., 16, 917-955 (2003)
    • (2003) J. Amer Math. Soc. , vol.16 , pp. 917-955
    • Lawler, G.1    Schramm, O.2    Werner, W.3
  • 35
    • 21044442631 scopus 로고
    • Statistical mechanics of probabilistic cellular automata
    • Lebowitz, J.L., Maes, C., Speer, E.R.: Statistical mechanics of probabilistic cellular automata. J. Stat. Phys. 59, 117-170 (1990)
    • (1990) J. Stat. Phys. , vol.59 , pp. 117-170
    • Lebowitz, J.L.1    Maes, C.2    Speer, E.R.3
  • 38
    • 0000378098 scopus 로고    scopus 로고
    • Blocking and persistence in zero-temperature dynamics of homogeneous and disordered Ising models
    • Newman, C.M., Stein, D.L.: Blocking and persistence in zero-temperature dynamics of homogeneous and disordered Ising models. Phys. Rev. Lett. 82, 3944-3947 (1999)
    • (1999) Phys. Rev. Lett. , vol.82 , pp. 3944-3947
    • Newman, C.M.1    Stein, D.L.2
  • 39
    • 0033070887 scopus 로고    scopus 로고
    • Equilibrium pure states and nonequilibrium chaos
    • Newman, C.M., Stein, D.L.: Equilibrium pure states and nonequilibrium chaos. J. Stat. Phys. 94, 709-722 (1999)
    • (1999) J. Stat. Phys. , vol.94 , pp. 709-722
    • Newman, C.M.1    Stein, D.L.2
  • 40
    • 0033728508 scopus 로고    scopus 로고
    • Zero-temperature dynamics of Ising spin systems following a deep quench: Results and open problems
    • Newman, C.M., Stein, D.L.: Zero-temperature dynamics of Ising spin systems following a deep quench: Results and open problems. Phys. A 279, 156-168 (2000)
    • (2000) Phys. A , vol.279 , pp. 156-168
    • Newman, C.M.1    Stein, D.L.2
  • 41
    • 2142835583 scopus 로고    scopus 로고
    • Private communication
    • Nienhuis, B.: Private communication (2001)
    • (2001)
    • Nienhuis, B.1
  • 42
    • 36149012281 scopus 로고
    • Crystal Statistics I. A two-dimensional model with an order-disorder transition
    • Onsager, L.: Crystal Statistics I. A two-dimensional model with an order-disorder transition. Phys. Rev. 65, 117-149 (1944)
    • (1944) Phys. Rev. , vol.65 , pp. 117-149
    • Onsager, L.1
  • 44
  • 45
    • 0000614574 scopus 로고    scopus 로고
    • Scaling limits of loop-erased random walks and uniform spanning trees
    • Schramm, O.: Scaling limits of loop-erased random walks and uniform spanning trees. Israel J. Math. 118, 221-228 (2001)
    • (2001) Israel J. Math. , vol.118 , pp. 221-228
    • Schramm, O.1
  • 46
    • 0010699019 scopus 로고    scopus 로고
    • A percolation formula
    • Schramm, O.: A percolation formula. Elect. Comm. Probab. 6, 115-120 (2001)
    • (2001) Elect. Comm. Probab. , vol.6 , pp. 115-120
    • Schramm, O.1
  • 48
    • 0041869040 scopus 로고    scopus 로고
    • Critical percolation in the plane: Conformal invariance. Cardy's formula, scaling limits
    • Smirnov, S.: Critical percolation in the plane: Conformal invariance. Cardy's formula, scaling limits. C. R. Acad. Sci. Paris 333, 239-244 (2001)
    • (2001) C. R. Acad. Sci. Paris , vol.333 , pp. 239-244
    • Smirnov, S.1
  • 49
    • 0035527905 scopus 로고    scopus 로고
    • Critical exponents for two-dimensional percolation
    • Smirnov, S., Werner, W.: Critical exponents for two-dimensional percolation. Math. Rev. Lett. 8, 729-744 (2001)
    • (2001) Math. Rev. Lett. , vol.8 , pp. 729-744
    • Smirnov, S.1    Werner, W.2
  • 52
    • 0000977505 scopus 로고
    • L'hypothèse du champ moléculaire et la proprieté ferromagnétique
    • Weiss, P.-E.: L'hypothèse du champ moléculaire et la proprieté ferromagnétique. J. de Phys. 6(4), 661-690 (1907)
    • (1907) J. de Phys. , vol.6 , Issue.4 , pp. 661-690
    • Weiss, P.-E.1


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