메뉴 건너뛰기




Volumn 224, Issue 3, 2001, Pages 733-781

Cube-root boundary fluctuations for droplets in random cluster models

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0035541772     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s220-001-8022-2     Document Type: Article
Times cited : (26)

References (28)
  • 1
    • 0000514175 scopus 로고
    • Stability of the Wulff minimum and fluctuations in shape for large finite clusters in two-dimensional percolation
    • 1. Alexander, K.S.: Stability of the Wulff minimum and fluctuations in shape for large finite clusters in two-dimensional percolation. Probab. Theory Rel. Fields 91, 507-532 (1992)
    • (1992) Probab. Theory Rel. Fields , vol.91 , pp. 507-532
    • Alexander, K.S.1
  • 2
    • 0031514908 scopus 로고    scopus 로고
    • Approximation of subadditive functions and rates of convergence in limiting shape results
    • 2. Alexander, K.S.: Approximation of subadditive functions and rates of convergence in limiting shape results. Ann. Probab. 25, 30-55 (1997)
    • (1997) Ann. Probab. , vol.25 , pp. 30-55
    • Alexander, K.S.1
  • 3
    • 0032045196 scopus 로고    scopus 로고
    • On weak mixing in lattice models
    • 3. Alexander, K.S.: On weak mixing in lattice models. Probab. Theory Rel. Fields 110, 441-471 (1998)
    • (1998) Probab. Theory Rel. Fields , vol.110 , pp. 441-471
    • Alexander, K.S.1
  • 4
    • 0035533095 scopus 로고    scopus 로고
    • Power-law corrections to exponential decay of connectivities and correlations in lattice models
    • 4. Alexander, K.S.. Power-law corrections to exponential decay of connectivities and correlations in lattice models. Ann. Probab. 29, 92-122 (2001)
    • (2001) Ann. Probab. , vol.29 , pp. 92-122
    • Alexander, K.S.1
  • 5
    • 0035633089 scopus 로고    scopus 로고
    • The asymmetric random cluster model and comparison of Ising and Potts models
    • 5. Alexander, K.S.: The asymmetric random cluster model and comparison of Ising and Potts models. Probab. Theory Rel. Fields 120, 395-444 (2001)
    • (2001) Probab. Theory Rel. Fields , vol.120 , pp. 395-444
    • Alexander, K.S.1
  • 6
    • 0002005827 scopus 로고
    • The Wulff construction and asymptotics of the finite cluster distribution for two dimensional Bernoulli percolation
    • 6. Alexander, K.S., Chayes, J.T. and Chayes, L.: The Wulff construction and asymptotics of the finite cluster distribution for two dimensional Bernoulli percolation. Commun. Math. Phys. 131, 1-50 (1990)
    • (1990) Commun. Math. Phys. , vol.131 , pp. 1-50
    • Alexander, K.S.1    Chayes, J.T.2    Chayes, L.3
  • 7
    • 0003118557 scopus 로고
    • Roughening transition, surface tension and equilibrium droplet shapes in a two-dimensional Ising system
    • 7. Avron, J.E., van Beijeren, H., Schulman, L.S. and Zia, R.K.P.: Roughening transition, surface tension and equilibrium droplet shapes in a two-dimensional Ising system. J. Phys. A 15, L81-L86 (1982)
    • (1982) J. Phys. A , vol.15
    • Avron, J.E.1    Van Beijeren, H.2    Schulman, L.S.3    Zia, R.K.P.4
  • 8
    • 0033443150 scopus 로고    scopus 로고
    • On the distribution of the length of the longest increasing subsequence of random permutations
    • 8. Baik, J., Deift, P. and Johansson, K.: On the distribution of the length of the longest increasing subsequence of random permutations. J. Am. Math. Soc. 12, 1119-1178 (1999)
    • (1999) J. Am. Math. Soc. , vol.12 , pp. 1119-1178
    • Baik, J.1    Deift, P.2    Johansson, K.3
  • 9
    • 0000393829 scopus 로고
    • Density and uniqueness in percolation
    • 9. Burton, R. and Keane, M.: Density and uniqueness in percolation. Commun. Math. Phys. 121, 501-505 (1989)
    • (1989) Commun. Math. Phys. , vol.121 , pp. 501-505
    • Burton, R.1    Keane, M.2
  • 10
    • 0033441652 scopus 로고    scopus 로고
    • On increasing subsequences of I.I.D. samples
    • 10. Deuschel, J.-D. and Zeitouni, O.: On increasing subsequences of I.I.D. samples. Combin. Probab. Comput. 8, 247-263 (1999)
    • (1999) Combin. Probab. Comput. , vol.8 , pp. 247-263
    • Deuschel, J.-D.1    Zeitouni, O.2
  • 11
    • 0031518868 scopus 로고    scopus 로고
    • Fluctuations of the phase boundary in the 2D Ising ferromagnet
    • 11. Dobrushin, R.L. and Hryniv, O.: Fluctuations of the phase boundary in the 2D Ising ferromagnet. Commun. Math. Phys. 189, 395-445 (1997)
    • (1997) Commun. Math. Phys. , vol.189 , pp. 395-445
    • Dobrushin, R.L.1    Hryniv, O.2
  • 12
    • 0003316893 scopus 로고
    • Wulff construction. A global shape from local interaction
    • Providence, RI: American Mathematical Society
    • 12. Dobrushin, R.L., Kotecký, R. and Shlosman, S.: Wulff construction. A global shape from local interaction. Translations of Mathematical Monographs 104, Providence, RI: American Mathematical Society, 1992
    • (1992) Translations of Mathematical Monographs , vol.104
    • Dobrushin, R.L.1    Kotecký, R.2    Shlosman, S.3
  • 13
    • 0001440863 scopus 로고
    • Generalization of the Fortuin-Kasteleyn-Swendsen-Wang representation and Monte Carlo algorithm
    • 13. Edwards, R.G. and Sokal, A.D.: Generalization of the Fortuin-Kasteleyn-Swendsen-Wang representation and Monte Carlo algorithm. Phys. Rev. D 38, 2009-2012 (1988)
    • (1988) Phys. Rev. D , vol.38 , pp. 2009-2012
    • Edwards, R.G.1    Sokal, A.D.2
  • 14
    • 0041855748 scopus 로고
    • On the random cluster model. I. Introduction and relation to other models
    • 14. Fortuin, C.M. and Kasteleyn, P.W.: On the random cluster model. I. Introduction and relation to other models. Physica 57, 536-564 (1972)
    • (1972) Physica , vol.57 , pp. 536-564
    • Fortuin, C.M.1    Kasteleyn, P.W.2
  • 15
    • 21344436631 scopus 로고
    • The stochastic random-cluster process and uniqueness of random-cluster measures
    • 15. Grimmett, G.R.: The stochastic random-cluster process and uniqueness of random-cluster measures. Ann. Probab. 23, 1461-1510 (1995)
    • (1995) Ann. Probab. , vol.23 , pp. 1461-1510
    • Grimmett, G.R.1
  • 16
    • 0031632711 scopus 로고    scopus 로고
    • On local behaviour of the phase separation line in the 2D Ising model
    • 16. Hryniv, O.: On local behaviour of the phase separation line in the 2D Ising model. Probab. Theory Rel. Fields 110, 91-107 (1998)
    • (1998) Probab. Theory Rel. Fields , vol.110 , pp. 91-107
    • Hryniv, O.1
  • 17
    • 0032270185 scopus 로고    scopus 로고
    • Dobrushin-Kotecký-Shlosman theorem up to the critical temperature
    • 17. Ioffe, D. and Schonmann, R.H.: Dobrushin-Kotecký-Shlosman theorem up to the critical temperature. Commun. Math. Phys. 199, 117-167 (1998)
    • (1998) Commun. Math. Phys. , vol.199 , pp. 117-167
    • Ioffe, D.1    Schonmann, R.H.2
  • 18
    • 0003067890 scopus 로고
    • Kinetic roughening of growing interfaces
    • (C. Godrèche, ed.) Cambridge: Cambridge University Press
    • 18. Krug, J. and Spohn, H.: Kinetic roughening of growing interfaces. In: Solids Far from Equilibrium: Growth, Morphology and Defects (C. Godrèche, ed.) Cambridge: Cambridge University Press, 1991, pp. 479-582
    • (1991) Solids Far from Equilibrium: Growth, Morphology and Defects , pp. 479-582
    • Krug, J.1    Spohn, H.2
  • 19
    • 0001440498 scopus 로고
    • Phase coexistence and surface tensions for the Potts model
    • 19. Laanait, L., Messager, A. and Ruiz, J.: Phase coexistence and surface tensions for the Potts model. Commun. Math. Phys. 105, 527-545 (1986)
    • (1986) Commun. Math. Phys. , vol.105 , pp. 527-545
    • Laanait, L.1    Messager, A.2    Ruiz, J.3
  • 22
    • 0001754757 scopus 로고
    • Divergence of shape fluctuations in two dimensions
    • 22. Newman, C.M. and Piza, M.S.T.: Divergence of shape fluctuations in two dimensions. Ann. Probab. 23, 977-1005 (1995)
    • (1995) Ann. Probab. , vol.23 , pp. 977-1005
    • Newman, C.M.1    Piza, M.S.T.2
  • 23
    • 0000842131 scopus 로고    scopus 로고
    • Directed polymers in a random environment: Some results on fluctuations
    • 23. Piza, M.S.T.: Directed polymers in a random environment: Some results on fluctuations. J. Statist. Phys. 89, 581-603 (1997)
    • (1997) J. Statist. Phys. , vol.89 , pp. 581-603
    • Piza, M.S.T.1
  • 24
    • 0001123141 scopus 로고
    • Existence and structure of solutions to a class of nonelliptic variational problems
    • 24. Taylor, J.E.: Existence and structure of solutions to a class of nonelliptic variational problems. Symp. Math. 14, 499-508 (1974)
    • (1974) Symp. Math. , vol.14 , pp. 499-508
    • Taylor, J.E.1
  • 25
    • 0000500627 scopus 로고
    • Unique structure of solutions to a class of nonelliptic variational problems
    • 25. Taylor, J.E.: Unique structure of solutions to a class of nonelliptic variational problems. Proc. Symp. Pure Math. 27, 419-427 (1975)
    • (1975) Proc. Symp. Pure Math. , vol.27 , pp. 419-427
    • Taylor, J.E.1
  • 27
    • 0022116584 scopus 로고
    • Inequalities with applications to percolation and reliability
    • 27. van den Berg, J. and Kesten, H.: Inequalities with applications to percolation and reliability. J. Appl. Probab. 22, 556-569 (1985)
    • (1985) J. Appl. Probab. , vol.22 , pp. 556-569
    • Van Den Berg, J.1    Kesten, H.2
  • 28
    • 0000484380 scopus 로고
    • Asymptotics of the Plancherel measure of the symmetric group and the limiting form of Young tables
    • 28. Vershik, A.M. and Kerov, C.V.: Asymptotics of the Plancherel measure of the symmetric group and the limiting form of Young tables. Dokl. Acad. Nauk. 233, 1024-1028 (1977)
    • (1977) Dokl. Acad. Nauk. , vol.233 , pp. 1024-1028
    • Vershik, A.M.1    Kerov, C.V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.